I hope that by the end of this answer you'll see why Matthew 10:28 almost certainly proves annihilationism(conditional immortality), or at the very least that it proves eternal conscious torment(henceforth ECT) to be wrong. We'll start with γεέννῃ(Gehenna).

What Is Gehenna?

The word for "Gehenna" in Greek is γεέννῃ(geennē). Jesus most likely used Gehenna as a symbol for the final eschatological judgment, i.e. the Second Death or Lake of Fire spoken of in Revelation 20. "Gehenna" is a transliteration of the Hebrew phrase "Ge-hinnom", which refers to the valley right outside Jerusalem. The valley is explicitly mentioned over 13 times in the Hebrew Bible as either "the Valley of the Ben-Hinnom"(Joshua 15:8; 18:16; 2 Kings 23:10; 2 Chronicles 28:3; 33:6; Jeremiah 7:31-32; 19:2; 6; 32:35), or "the Valley of Hinnom"(Nehemiah 11:30). And there are several allusions to the valley, the most prominent being Jeremiah 31:40 and Isaiah 66:24. We'll analyze substantial mentions of Ge-hinnom in the Hebrew Bible.

But first, I want to clear something up. It's a very popular notion that Gehenna refers to a perpetually burning garbage dump in the Valley of Hinnom. However, this notion has very little evidence to support it. See these articles here and here. So, what was Jesus talking about when He used "Gehenna"? For that, we have to go to the Hebrew Bible(that which Jesus was fully steeped in throughout His life).

In 2 Chronicles 28:3, we see that King Ahaz sacrificed his children in the fire in Ge-hinnom(c.f. 2 Kings 16:3). Manasseh, like his grandfather Ahaz, also burned his children in Ge-hinnom(2 Chronicles 33:6; c.f. 2 Kings 21:6). Jeremiah 32:35 tells us that "they built high places for Baal in the Valley of Ben Hinnom to sacrifice their sons and daughters to Molech," something Yahweh never commanded, nor did it enter His mind, that they should do such a detestable thing and make Judah sin. Manasseh had "shed very much innocent blood, till he had filled Jerusalem from one end to another"(2 Kings 21:16). Because of this, Yahweh decided to bring massive calamity upon Jerusalem and Judah(2 Kings 21:12). When Josiah(Manasseh's grandson) took the throne, he reformed Judah(2 Kings 23:1-25). 2 Kings 23:10 says that Josiah "desecrated Topheth, which is in the Valley of the Son of Hinnom, that no one might burn his son or his daughter as an offering to Molech." We see that Tophet was the place of fire within the Valley of Ben-Hinnom where child sacrifices took place. Josiah ensured that no one would sacrifice their children in the Valley of Ben-Hinnom by wrecking it.

Already, we see that Ge-hinnom is a site of death and desolation, and due to the atrocities of human beings at that. It is because of these depravities committed in the Valley of Hinnom that Yahweh decided to turn it against them and let Ge-hinnom serve as a place of the judgment that would be brought upon them by Him; the place where they once perpetrated horrific acts is now the place where God has brought heavy judgment upon them. This is seen plainly in Jeremiah, where Ge-hinnom is portrayed as a place where the apostate Israelites will be utterly eliminated by Yahweh.

[Jeremiah 7:30-34] For the sons of Judah have done that which is evil in My sight,” declares the Lord. “They have put their detestable things in the house which is called by My name, to defile it. 31 They have built the high places of Topheth, which is in the Valley of Ben-Hinnom, to burn their sons and their daughters in the fire, which I did not command, and it did not come into My mind. 32 “Therefore, behold, days are coming,” declares the Lord, “when it will no longer be called Topheth, or the Valley of Ben-Hinnom, but the Valley of the Slaughter; for they will bury in Topheth because there is no other place. 33 The dead bodies of this people will be food for the birds of the sky and for the animals of the earth; and no one will frighten them away. 34 Then I will eliminate from the cities of Judah and from the streets of Jerusalem the voice of joy and the voice of gladness, the voice of the groom and the voice of the bride; for the land will become a site of ruins.

All this certainly invokes pictures of complete eradication and decimation. Ge-hinnom will be called the "Valley of Slaughter", filled to the brim with the corpses of those who have done vile and despicable things(i.e. burn their children alive in honour of false deities), rotting in oblivion and being decomposed by scavengers(birds of the sky and animals of the land); the intense language gives us the image of a bloody battle scene of utmost desolation, with no survivors and dead bodies laid out in the open. This same language with reference to Ge-hinnom is employed again in Jeremiah 19. Here are the highlights(but read the whole chapter);

[Jeremiah 19:2; 6-7] Then go out to the Valley of Ben-hinnom, which is by the entrance of the Potsherd Gate, and proclaim there the words that I tell you,; therefore, behold, days are coming,” declares the Lord, “when this place will no longer be called Topheth or the Valley of Ben-hinnom, but rather the Valley of Slaughter. 7 And I will frustrate the planning of Judah and Jerusalem in this place, and I will make them fall by the sword before their enemies and by the hand of those who seek their life; and I will make their carcasses food for the birds of the sky and the animals of the earth.

Again, the images of death and destruction, with the carcasses of the Israelites who were smitten by the sword of their enemies laid out in the open for scavengers to finish them off.

Next is Jeremiah 31:40, which undoubtedly alludes to Ge-hinnom when it refers to the "valley of dead bodies and ashes" near the Kidron(which is right next to the Valley of Hinnom). Ge-hinnom is a "valley of dead bodies and ashes" because it is a place where those who have done despicable things are slain and left out in the open to be consumed either by scavengers or by fire(hence the "ashes").¹ The next unmistakable allusion to Ge-hinnom is perhaps the most significant, as it is the text most alluded to by Jesus when He speaks about Gehenna. It is Isaiah 66:24. The 66th chapter of Isaiah describes an eschatological battle scene outside of Jerusalem, where Yahweh protects the righteous within the city while massacring the wicked who have rebelled against Him(see v.3-4).

[Isaiah 66:15-16] For behold, Yahweh will come in fire, and his chariots like the whirlwind, to render his anger in fury, and his rebuke with flames of fire. 16 For by fire will Yahweh enter into judgment, and by his sword, with all flesh; and those slain by the Lord shall be many.

The final verse(v.24) shows us the aftermath of God's judgment; a pile of corpses being totally consumed by an unstoppable blaze, the leftovers for the decomposers(worms/maggots).²

[Isaiah 66:24] Then they will go out and look at the corpses of the people who have rebelled against Me. For their worm will not die and their fire will not be extinguished; And they will be an abhorrence to all mankind.” (NASB)

These images of death and destruction are the ones being conjured in the minds of Jesus' disciples when He employs Gehenna in His teachings. Ge-hinnom is nowhere associated with "spiritual death"(separation from the presence of God); only physical death(separation between body and life-breath/spirit). That Jesus would use Ge-hinnom, a place notorious in the Hebrew Bible for the brutal destruction of God's enemies, to signify a concept(i.e. eternal conscious existence separated from God) that is not only never once associated with Ge-hinnom in the Hebrew Bible but also completely opposed to the notions explicitly and incontrovertibly portrayed by Ge-hinnom is absurd, to say the least. That Jesus' disciples, entirely unfamiliar with the notion of eternal conscious separation(on account of the fact that such a notion is not explicitly[or even implicitly] found anywhere in the Hebrew Bible) and thoroughly acquainted with the notion of God slaying His enemies(especially with regard to Ge-hinnom, as seen by the aforementioned), would have ever believed such a thing, beyond absurd.³

What Does Matthew 10:28 Mean?

Matthew 10:28 Do not be afraid of those who kill the body but cannot kill the soul. Instead, fear the One who can destroy both soul and body in Gehenna.

1. [Do not be afraid of those who kill the body]

"Those" refers to men(human beings). Men "kill the body". The word for "kill" is ἀποκτείνω(Strong's G615), and the word for "body" is σῶμα(Strong's G4983). This is the only place in the entire Bible where such an expression("kill the body") appears. The Bible talks only about killing persons, never bodies. Bodies are never said to be "living"; only people are said to be "living". If bodies are not living things, how can we kill them(cause their life to cease to exist)? I realized that, in a sense, bodies are alive(though not exactly as people are). I mean, bodies do things; they have abilities. Functional bodies are equipped with sentience(that goes for [most] animals too) and numerous capabilities, such as the capability to pump blood throughout your body using your heart, the capability to walk or talk or use any of your various senses(by the way, there are more than five), and especially the capability to breathe, that is, to hold the breath of life within(when the capability to breathe is abolished, the vital life-breath returns to the One who gave it[and the person returns from whence they came, that is, to the dust{which is a metaphor for returning to the inert and lifeless state we were once in before God put our breath into us}], until He is ready to reinsert it into us). So, while our bodies are not the whole of us, they are still alive in the sense that they operate and function, i.e. they are animate and active(even when we are asleep).

Our bodies are not inert or powerless; though they can be. And men can cause this(say by plunging a sword through someone's heart). Men have the capacity to cause our bodies(our brain, heart, lungs, etc.) to shut down(and we lose the ability to respire). This act directly correlates to our death(or our life-breath separating from our body). When the body becomes incapable of doing anything, our life-breath leaves it to go to God. When we say "dead body", we mean "body of a dead person", but in a sense, the body is also dead too because it is completely powerless and inert; without the capacity to do anything(incapacitated). Thus, that is what Jesus is saying; that men have the capacity to shut down our bodies, that is, to cause our bodies to be fully impotent and inactive, unable to perform anything at all; they can cause our bodies to be fully nonfunctional. Hence, Jesus is using "kill"(ἀποκτείνω) here in the sense of causing to become inert, powerless, nonfunctional.

But Jesus is also telling us not to be afraid of that. But why? Well, because there is more to a human than the tangible, material part of them. There is also an intangible, immaterial part of a person, which is their vital life-breath; the force that sustains their life. It was the item that God conferred onto Adam at Genesis 2:7. Although you cannot see it or feel it or measure it, it's there; and it goes back to God upon the cessation of someone's life(see Psalm 104:29, Psalm 146:4, Ecclesiastes 12:7, Job 34:14-15, Luke 23:46, Acts 7:59). It is this vital life-breath that God puts back into a person upon resurrection(see Ezekiel 37:5-6). And it is what men cannot touch; when the body dies, the life-breath retains all of its life-giving properties and can be put back into a viable/usable body at any moment(see Luke 8:54-56). It is for this reason that we should not fear men. The worse they can do is temporarily deprive us of our life by destroying our functional bodies, that is to say, when they kill, the effects of their killing are not everlasting; God can put our life-breath(which remains untouched when humans kill us) back into us at the resurrection.

2. [but cannot kill the soul]

Matthew's use of the conjunction δὲ(but) denotes that what Jesus is saying here is in contrast to His previous statement(do not be afraid of those who kill the body). That is to say, Jesus is expressing that what man can do to the "body"(σῶμα) is what man cannot do to the "soul". The word for "soul" is ψυχή(Strong's G5590). Jesus uses the exact same word(ἀποκτεῖναι) to describe the killing of the soul(ψυχή) that He had just used 4 words ago(half a second ago) to describe the killing of the body(σῶμα). Do you think Jesus switched from one definition of ἀποκτεῖναι to another in half a second? That when referencing the body, He's talking about one kind of "killing", but when referencing the soul, He's talking about another kind of "killing"(namely, "spiritual killing"/"separation from the presence of God")? Or do you think that Jesus, in using the exact same word within the exact same context merely half a second apart, is talking about the same type of killing when referencing both the body and soul? So, in what sense was Jesus using "kill"(ἀποκτεῖναι) when He talked about the body? We already determined that it was in the sense of causing to become inert, powerless, nonfunctional. Indeed, to paraphrase from this answer here: "We can claim they both describe [causing to become nonfunctional/powerless], or they both describe [separating from the presence of God], but creating a hybrid where the verb changes meaning within this single chreia would entirely miss the point Jesus is making about what men can & cannot do."

Now, what exactly is the identity of this mysterious ψυχή? Is it the immortal conscious soul? Is it the life of a person? Is it the spirit/life-breath of a person? Is it the mind/inner-being of a person(without the immortality part)? I don't suppose there's any way to know for sure, but it matters not, because we know the most important thing; whatever the ψυχή is, we know Matthew 10:28 is saying that men cannot do to it what they can do to the body, i.e. that men cannot cause the ψυχή to become powerless/lifeless and nonfunctional(as they can with the body). That is what we know for sure; separation from God is NOT in view. Unless, of course, in the act of separating the ψυχή from God, it becomes wholly powerless and nonfunctional. But those who believe in ECT do not believe that the ψυχή becomes nonfunctional; merely that it's "rendered useless, unable to fulfil its primary purpose"(which apparently entails "being deprived of love and a relationship with God", even though that is a non-sequitur). The ψυχή of a person(operating under the notion of the soul[immortal inner-being]) still retains consciousness/awareness and the ability to think and feel emotion(albeit emotions of misery and desperation, but emotion nonetheless); hence not entirely inoperative(a dead body, however, is fully inoperative; incapable of doing anything at all whatsoever). Personally, I think that ψυχή refers to the breath of life in Matthew 10:28; it's the most natural reading(Jesus is contrasting the body and ψυχή of a person; body and spirit are what make up a living person). Hence, Jesus is saying that men do not have the ability to make the life-breath powerless/nonfunctional(i.e. they cannot cause it to altogether lose its life-giving properties).

3. [Instead, fear the One who can destroy both soul and body in Gehenna]

The word used for "destroy" is ἀπόλλυμι(Strong's G622). I thoroughly analyze the word "ἀπόλλυμι" in my answer here. In short, ἀπόλλυμι never indisputably refers to "separating from the presence of God"(not that that would help ECT much, as I point out in my posts here and here), and when ἀπόλλυμι refers to "rendering unusable/useless", it's always with reference to inanimate, lifeless objects(there's no evidence it has such a usage with regards to living beings[e.g. humans]). But it's not like that matters anyway, as we will see. Jesus is clearly is making a contrast between the power/ability of God and the power/ability of men. Jesus is saying that what men CANNOT do, God CAN do; that is why He says, instead. He wants us to fear God instead of men because He(God) can do what they(men) cannot. What was it, again, that they could not do? Was it that men could not cause the ψυχή to be separated from the presence of God? Was it that they could not render it useless? Jesus said that men could not "kill"(that is, "render powerless and nonfunctional") the ψυχή(as they can with the body). So what Jesus is saying is that God has the capacity to render the life-breath totally inert, powerless, and inoperative, while men do not; hence we should fear Him rather than men. The right reading of this passage is this: What men can do to the body, but cannot do to the life-breath/spirit, God can do to both the body and life-breath/spirit in Gehenna, and hence we should fear Him rather than men. Men can cause the body to be entirely powerless/nonfunctional, but they cannot cause the life-breath to become powerless/nonfunctional; the life-breath returns to God, retaining all its life-giving properties, waiting until it can be reinserted into a person so as to restore them to life. In Gehenna, however, God can cause the life-breath to lose all its power and ability; to become entirely nonfunctional. Essentially, God can nullify/make void the vital life-breath in Gehenna, and(Gehenna signifying final eschatological judgment) He can do so with permanent(everlasting) effects. All this to say that God can cause the two components(body and life-breath) necessary to create a functional, animate being to become permanently nonfunctional(deprived of all their capabilities), making resurrection(which demands a functional body and life-breath/spirit) an impossibility in perpetuity, thereby rendering the person dead(and unconscious)⁴ for eternity. God can cause the everlasting "shut-down" of our existence, and accordingly, we fear Him. That is what Matthew 10:28 is saying!

Notes:

_{1. Historically, the two most common methods by which a dead body was disposed of were cremation and burial. When a body was cremated, it was turned to ashes(reduced to nothing). When a body was buried, decomposers such as maggots(and of course, many types of bacteria) would over time consume the dead flesh, eventually leaving nothing behind but bones(as for bodies left in the open, scavengers such as vultures, coyotes, or hyenas would feast on the dead flesh, again leaving nothing behind but bones).}

_{2. That "worm"(תּוֹלֵעָה) can refer to a "maggot" or "wormlike larvae that feasts on carrion" is evident by the way it is paralleled with the Hebrew word for "maggot"(רִמָּה) in Job 25:6 and Isaiah 14:11.}

_{3. Here's something to think about. If God genuinely hated sin, wouldn't He, like, put an end to it someday? Guaranteeing that sin endures for eternity by resurrecting those who perpetrate it in immortal, incorruptible bodies doesn't seem like something a God who despises sin would do; it certainly sounds like something a God who relishes sin would do. Usually, when people hate something, the last thing they would want to do is deliberately ensure its eternal existence. Just a thought.}

_{4. But why unconscious? Aren't the dead conscious? Sure, let's assume they are. People who believe in post-mortal death do so because they believe that the "conscious spirit" or "soul" lives on after death, correct? Well, if in Gehenna God causes the "conscious spirit/soul" to become inactive and nonfunctional, what is left with regards to being conscious? The whole reason there is consciousness after death is because the conscious spirit/soul lives on, remaining intact. But if God makes the spirit/soul void in Gehenna, how could those who are cast into Gehenna possibly be conscious? Both their body and their soul/spirit are entirely lifeless and inoperative, without the capacity to do anything, hence there is no room for any conscious experience(let alone the conscious experience of eternal torment).}