Does the right side have a higher status than the left?

What you are seeing here is custom, not necessarily what God elevates.

Put crassly, to the Bible writers, the left hand was what you wiped your bum with, not what you would present to a guest if you were being hospitable.

Jesus warns in Luke 14, for example, that:

: 8“When someone invites you to a wedding feast, do not take the place of honor, for a person more distinguished than you may have been invited. 9If so, the host who invited both of you will come and say to you, ‘Give this person your seat.’ Then, humiliated, you will have to take the least important place. 10But when you are invited, take the lowest place, so that when your host comes, he will say to you, ‘Friend, move up to a better place.’ Then you will be honored in the presence of all the other guests. 11For all those who exalt themselves will be humbled, and those who humble themselves will be exalted.”

That place of honor would naturally have been the seat to the right of the host. That was simply the custom.

Likewise, we are told in Mark 16 that:

After the Lord Jesus had spoken to them, he was taken up into heaven and he sat at the right hand of God.

Again, the right hand of God was simply the place of honor. As such, being the very Son of God, he would naturally have been placed there.

The lesson that Christians take from all of this, however, is that understanding Jesus to be at the head, we ought not to worry about our position of honor. Whether Left or Right, we ought to honor all. In 1 Corinthians 12, the Apostle Paul writes:

22 On the contrary, the parts of the body that seem to be weaker are indispensable, 23 and on those parts of the body that we think less honorable we bestow the greater honor, and our unpresentable parts are treated with greater modesty, 24 which our more presentable parts do not require. But God has so composed the body, giving greater honor to the part that lacked it, 25 that there may be no division in the body, but that the members may have the same care for one another. 26 If one member suffers, all suffer together; if one member is honored, all rejoice together. 27 Now you are the body of Christ and individually members of it.

I think the "right" side have a higher status simply because the most people are right-handed.

We read some passages where lefties have an advantage in surprising the enemy, as in Ehud's history

15 But when the children of Israel cried unto the Lord, the Lord raised them up a deliverer, Ehud the son of Gera, a Benjamite, a man lefthanded: and by him the children of Israel sent a present unto Eglon the king of Moab.

16 But Ehud made him a dagger which had two edges, of a cubit length; and he did gird it under his raiment upon his right thigh.

17 And he brought the present unto Eglon king of Moab: and Eglon was a very fat man.

18 And when he had made an end to offer the present, he sent away the people that bare the present.

19 But he himself turned again from the quarries that were by Gilgal, and said, I have a secret errand unto thee, O king: who said, Keep silence. And all that stood by him went out from him.

20 And Ehud came unto him; and he was sitting in a summer parlour, which he had for himself alone. And Ehud said, I have a message from God unto thee. And he arose out of his seat.

21 And Ehud put forth his left hand, and took the dagger from his right thigh, and thrust it into his belly

Judges 3:15-21

also in the case of Benjamin's Tribe

"Among all this people there were seven hundred chosen men lefthanded; every one could sling stones at an hair breadth, and not miss." Judges 20:16

Perhaps you are wondering about the tortures of the Middle Ages:

One of the most accepted theories to justify the preference for the right side of things says that came with the primitive inhabitants of the northern hemisphere. For the sun worshipers the northern hemisphere, the sun appears to move clockwise to the right. Following in this vein, Buddhists make their treks to meditate; pilgrims who go to Mecca to pray Allah surround the estluertici right the Kaaba, where the construction is the sacred stone of Mohammed's followers. Muslims, in fact, go so far as to state that God has two right hands.

Also in the Middle Ages left hand happens to be related to the dirt. The explanation for this until we have some logic: a period when washing up was a rare habit, cleanliness was due to the left hand, including personal hygiene . Afraid to get dirty, people just shook hands with the right hand, the same used for eating or combing hair .

At the time of giving his word , the Greek was the one who was in favor of the left: "aristera", the Greek term for the left hand , has the meaning of "best" and the same origin of the word aristocracy. Latin, at first, agreed with this positive image : sinister , whatever "left" say , meant "Lucky" , the word comes from "sinus", the pocket of the Roman toga which was, of course, that side .

But this was the era in which the statues of the Roman gods had to face south and look directed to the left , to the east , where they came from , with the sun , the signs of good fortune . Do not know why, but images of deities, approximately the second century, were directed to the north. Hence the east was right. From "Lucky" the word "sinister" came to be "unlucky" and the Romans began to sew your pockets on the right side.