Why were early Mormon leaders so critical of traditional Christianity?

Mason's answer is excellent, but I'm one of those mormons who tends to give it to people straight.

The perfectly candid answer to your question, "why did the early leaders say those things about traditional christianity?" is, "because it's the truth".

This isn't the kind of stuff that's preached over the pulpit in LDS churches (at least not anymore), coming closer to Christ and showing charity and love to your fellow man are the norm in most meetings, but I think we live in a world where more people need to hear the hard truth.

[...] Behold there are save two churches only; the one is the church of the Lamb of God, and the other is the church of the devil; wherefore, whoso belongeth not to the church of the Lamb of God belongeth to that great church, [...] (1 Nephi 14:10)

Many modern sects of traditional Christianity would have you believe that as long as you believe, that's good enough, that it doesn't matter which church you belong to, as long as you're a good person, read the Bible, and keep the commandments. Some even go as far as to say that as long as you're "saved" (you've accepted Christ as your Saviour) then it doesn't matter what you do for the rest of your live because everyone that is "saved" goes to heaven.

These are all clever and malicious lies created by the Devil himself. The truth is that there is only one true church of Jesus Christ. The rest are schisms of a church founded by the devil with the clandestine purpose of bringing the souls of men close enough to Christ to convince them they are following Him, while denying them the essential life saving ordinances necessary to be saved in the kingdom of God.

And it came to pass that I saw among the nations of the Gentiles the formation of a great church. And the angel said unto me: Behold the formation of a church which is most abominable above all other churches, which slayeth the saints of God, yea, and tortureth them and bindeth them down, and yoketh them with a yoke of iron, and bringeth them down into captivity. And it came to pass that I beheld this great and abominable church; and I saw the devil that he was the founder of it. (1 Nephi 13:4-6)

Satan desires nothing more than to destroy the souls of men, and to accomplish his goals he devised a very cunning plan. By mingling the doctrines of God with false doctrines, he created an institution of religion whose followers reject the true messengers of God by convincing themselves they already have the truth, and that the true messengers, sent by Christ himself, are evil.

Satan allowed this church to maintain 90% of the truth, but denied them many plain and precious doctrines which are essential for salvation and exaltation. I'm sure you've heard the old adage, "The best lie is 9/10ths truth." Satan was the first to realize this.

I used to wonder why Satan even tried, I figured he had to know that he didn't stand a chance against God Almighty, why even put forth the effort? Now that I've grown wiser it's obvious to me that Satan has been gaining ground for thousands of years. Every year the world grows more wicked, look at the world we live in today, religion has been removed from government, from schools, Christians are persecuted for upholding traditional family morals, and abominable sins against nature are being embraced by the world as pure, wholesome and good.

The Christianity which was established and grew during the Great Apostasy was a deadly trap laid by the Devil, designed to ironically keep those that desired to follow Christ away from His true Church. This is why the LDS church spends so much time doing missionary work with other Christian denominations, because we know the desire to serve Christ is in their hearts, they've heard the good news, and they want more than anything return to the Father in Heaven, but they are ignorant to the fact that they have damned themselves by uniting with a Church that does not hold Christ's authority to preform essential saving ordinances. They must accept God's living Prophets, and be baptized into the Church of Jesus Christ of Latter-Day Saints, which is the only Church on earth today unto which Christ has given authority to minister to the world.

The central piece of theology that all these revolve around can be found in the third statement cited:

Nothing less than a complete apostasy from the Christian religion would warrant the establishment of the Church of Jesus Christ of Latter-day Saints

This is one of the core points of LDS theology: that the apostasy spoken of by Paul, the "famine of hearing the words of the Lord" that Amos prophesied, has already occurred. With intense persecution bringing about death of the Apostles faster than they could organize to choose new ones, eventually the unbroken line of authority was lost, and the Church began to lose its grip on the doctrine. The historical record suggests that this happened alarmingly quickly: the second-century Christian author Iranaeus wrote a series of five books to refute the teachings of multiple different Gnostic sects that were beginning to take strong root within the church already!

Wherever the Great Apostasy began, it's hard to look at the history of the Church without seeing evidence that it was complete at some point around the conversion of Constantine, if not before it then very soon afterwards. With the high honors the State heaped upon the Christian religion, with authority in the Church becoming one of the fastest and surest routes to political power, it's hard to say with a straight face that the organization of schemers that emerged in this period was the same one set up by He who said "my kingdom is not of this world"! ("Where shall we look for the true order or authority of God? It cannot be found in any nation of Christendom.")

This puts another quote by Brigham Young in perspective, by the way:

The worst fear that I have about this people is that they will get rich in this country, forget God and his people, wax fat, and kick themselves out of the Church and go to hell. This people will stand mobbing, robbing, poverty, and all manner of persecution, and be true. But my greater fear for them is that they cannot stand wealth.

-- Brigham Young: The Man and His Work, 4th ed., p.126-129

By the sixth century, the Athanasian Creed had emerged in common worship, which defined the "necessary" faith as believing in the Trinity, "the Father incomprehensible, the Son incomprehensible, and the Holy Spirit incomprehensible." If we take John 17:3, which equates eternal life with knowing God and Jesus Christ, at face value, a disturbing contradiction emerges: the Church had somehow come around to a position in which it dogmatically defined as necessary for the salvation of all believers to hold a belief that would in fact disqualify them from salvation! ("What is it that inspires professors of Christianity generally with a hope of salvation? It is that smooth, sophisticated influence of the devil, by which he deceives the whole world")

With the true Church in apostasy, many reformers attempted to use their knowledge and scholarship to piece together the true principles of the Gospel, but without the lost line of authority, their answers could only get so far. None of the Reformers even managed to set up the organization described by Paul in Ephesians chapter 4, and the problems he spoke of in the same passage are quite instructive:

11 And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers;

12 For the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ:

13 Till we all come in the unity of the faith, and of the knowledge of the Son of God, unto a perfect man, unto the measure of the stature of the fulness of Christ:

14 That we henceforth be no more children, tossed to and fro, and carried about with every wind of doctrine, by the sleight of men, and cunning craftiness, whereby they lie in wait to deceive;

There could really only be one solution. If we turn the quote from Joseph Smith around, it implies what that solution is: A complete apostasy from the Christian religion would require the establishment of the Church again, by restoration rather than reformation, which is the central message of Mormonism: that original Christianity was restored by revelation and authority from God, as it was originally founded by revelation and authority from God, with apostles and prophets to lead it as in ancient days. The basic meaning of all the quotations cited in the question above is simply this: that the fulness of the restored gospel can only be found in one place, and that any other religion, no matter how sincere or how hard they may genuinely try to get the Gospel and the requirements for salvation right, is missing necessary details, the absence of which will hold their adherents back.