What were Martin Luther's main disagreements with the Catholic Church?

The main disagreements between Luther's understanding of Christianity and the Roman Catholic church's teachings concerned the way in which we're counted righteous in God's sight, whether we have free will in our unregenerate state to respond affirmatively to God, and whether the Scriptures alone are the final authority to determine Christian doctrines. Luther held that the Christian church is dependent on Scripture as the Word of God, and that the papacy was based on a faulty understanding of various Scripture verses. Secondly he held on the basis of Scripture that conversion isn't something we can contribute to but is wholly the work of the Holy Spirit who enlightens with the saving knowledge of Christ who He will. And thirdly the way in which we become righteous in God's sight isn't through our own personal endeavours but is through God accounting us righteous because of our faith in Christ, who atoned for our sins.

In one of Luther's sermons he describes the situation that existed before he became acquainted with the truth which explains the darkness which people were living under prior to the Reformation:

….the miserable pope has contributed a great deal with his doctrines, ordinances, and laws, causing pious hearts to be greatly terrified by proclaiming that it is necessary to pray, fast, hear masses, make pilgrimages, and that it is a mortal sin if they fail to do this. Terrorized like this, nobody could know when enough is enough, because true comfort, forgiveness of sins through Christ, had disappeared completely. As a result people ran to St. James and tormented themselves with pilgrimages, fastings, and other works, to the point in my estimation that there could not have been a greater misery on earth. I myself have seen many who were unable to bear such deep anguish, on account of which they fell into despair through intense fear and terror, and were seized with horror before God's dreadful judgment. For by his preaching the pope had nearly succeeded in scaring us to death of Christ; we considered him to be a stern judge. I, too, had been one of those who expected Christ to be nothing more than a severe master, and as a result I called on the Virgin Mary to stand by me and be my advocate before this judge. Others did the same thing because that was all they knew. We all said, The judge is coming, the judge is coming; I have been a bad boy, help, dear Virgin Mary, otherwise there is neither comfort nor help nor counsel for my poor soul. That's how we babbled, and people did not know what else to do. For they had lost Christ, the true and only Saviour. (Pages 46,47, Vol V, Complete Sermons of Martin Luther, Baker Book House, 2007)

The Lutheran church came into existence because it proved impossible to reform the papist church. The latter continued to insist that it was truly Catholic and that Luther, and those who agreed with him, were heretics (instead of being in reality the true Catholics), so there was no other option but for Luther to separate from the church controlled by the popes. This then led to the formation of the Lutheran church (i.e. not to be confused with present day Lutheran churches which have diverged from Luther's teachings to a greater or lesser extent). Luther explained in his Table Talk why he separated from the popes:

The chief cause that I fell out with the pope was this: the pope boasted that he was the head of the church, and condemned all that would not be under his power and authority; for he said, although Christ be the Head of the church, yet, notwithstanding, there must be a corporal head of the church upon earth. With this I could have been content, had he but taught the Gospel pure and clear, and not introduced human inventions and lies in its stead. Further, he took upon him power, rule, and authority over the Christian church, and over the Holy Scriptures, the Word of God; no man must presume to expound the Scriptures, but only he, and according to his ridiculous conceits; so that he made himself lord over the church, proclaiming her at the same time a powerful mother, and empress over the Scriptures, to which we must yield and be obedient; this was not to be endured. They who, against God’s Word, boast of the church’s authority, are mere idiots. The pope attributes more power to the church, which is begotten and born, than to the Word, which has begotten, conceived, and borne the church. We, through God’s grace, are not heretics, but schismatics, causing, indeed, separation and division, wherein we are not to blame, but our adversaries, who gave occasion thereto, because they remain not by God’s Word alone, which we have, hear, and follow. CCCCLIII, Table Talk, translated by William Hazlitt.