Before Luther wrote his Ninety-Five Theses, a couple of theologians directed fundamental criticisms at the Catholic Church. First, in the 14th century, John Wycliffe questioned the status and rituals of the clergy in England, and later, in the 15th century, Jan Hus made similar arguments. Wycliffe would be deemed a heretic, and his followers were pejoratively referred to as "Lollards." Likewise, Jan Hus was burned at the stake for his heresy. Granted, Hus' followers did respond by fighting the eponymous Hussite Wars, but they were ultimately unsuccessful. However, in the 16th century, the Catholic Church would finally meet an intractable opponent in Martin Luther. Despite incurring the ire of the Catholic Church and Holy Roman Empire, Luther's critiques would serve as the basis for the Protestant Reformation, and initiate what at that point was the greatest "thought revolution" in European history. Protestantism spread throughout northern and central Europe, even outside of Luther's native Germany. In contrast to being burned at the stake, Luther would die of natural causes as a free, venerated man. My question could be phrased in a few ways, but I think I'm basically getting at this: Why did Luther's critiques — as opposed to those of Wycliffe and Hus — become the foundation for the rupture of the Catholic Church? How was he able to evade the threats posed by the Church, and why did his ideas spread so widely and resonate so strongly? Had something about Europe changed by this point compared to the periods in which Wycliffe and Hus lived, or was there something about Luther's critiques that were fundamentally different and more appealing?
I have written answers to this question before here and elsewhere, which I will repost below. The short answer is that yes, Germany in the early 16th century was a different place than England in the late 14th or Bohemia in the early 15th.
The classic answer is that the difference was a combination of the development of printing and some critical political changes in Europe. More recent scholarship has brought a bit more nuance to that answer, looking more at social and cultural issues, but I think the basic thesis still holds water.
The importance of printing cannot be overstated. I tell my students that it was at least as revolutionary as the internet. I recently wrote an answer to this question about the cost of books before printing. The short answer is that even the smallest, plainest book would have cost the equivalent of at least a couple months' wages for a skilled worker. By way of contrast, Luther's 95 Theses were printed by the thousands in the months after their publication. Printing allowed ideas to spread far faster than they ever had before. Wycliffe could write a text, but until someone took the time to copy it out by hand, only one person could read it at a time. Hus could give a sermon, but only the people actually in the church were likely to ever hear exactly what he had to say. By the time news of the new controversy in Wittenburg reached the pope in early 1518, the original Latin version of the Theses had been printed in (at least) Wittenburg, Nuremburg, Basel, and Leipzig, and had already been translated into German and begun to circulate in that language as well.
Printing also made it practically impossible to effectively ban books and destroy every copy. There were simply too many copies of popular texts to ever track them all down, unless they were seized directly from the publisher before they could be distributed (as did actually happen with at least one early printing of the 95 Theses). On the other hand, we know relatively little about actual Cathar beliefs and practices, because few of their texts have survived. The movement never really spread far beyond southern France and northern Italy, there probably were relatively few copies of their books to begin with, and most of the books that did exist were lost or destroyed during the Albigensian crusade and subsequent inquisition. Most of what we know about the Cathars comes from writings by their opponents. Likewise, in the 12th century a man named Arnold of Brescia was repeatedly condemned and ultimately executed. The order to destroy all his writings was carried out so thoroughly that none of them have survived in any form. We don't even know what was in them. We only know he even existed from the writings of his opponents; supposedly he taught that clergy should not own property. But whatever he wrote, there were so few copies of it that all of them were lost or destroyed in the 12th century.
We also need to consider the political situation. The early 16th century was a time of growing political power for secular rulers. Centralized governments that looked more like modern states than medieval feudal societies were just beginning to develop in some places. The reasons for this are complex and beyond the scope of your question. Just know that kings, dukes, princes, etc., were eager to jump at anything that might strengthen their position (see Henry VIII of England). The Catholic Church still held a lot of power in Western Europe, and an astute ruler who was quick on his feet and just lucky enough could stand to gain some of that power if he played his cards right.
The situation in Germany at the time was such that much of the power was in the hands of local rulers. Luther lived in Saxony, which was ruled by Prince Frederick, an imperial elector. He was one seven electors who had the responsibility of choosing the next Holy Roman Emperor when the old one died or abdicated. In practice, the office was in the process of becoming a hereditary possession of the Habsburgs, but the position of elector was still an important one. In addition to this responsibly, Saxony had imperial immediacy, meaning that its prince was subject to the emperor directly, not to an intermediary noble who himself was subject to the emperor. All this made Frederick (known to protestants today as "Frederick the Wise") one of the most powerful people in Germany. He had the ability to protect Luther, even against the wishes of the pope and emperor. He arranged for Luther to have a promise of safe passage to his trial in Worms in 1521, and ensured that the promise was kept. Luther was condemned as an outlaw at his trial (literally meaning outside the protection of the law, so he could be robbed or killed with impunity) and it was strictly forbidden for anymore to give him any shelter or aid, but he was nonetheless allowed to leave the city. Frederick then arranged for Luther to disappear on his way back home, and hid him in a castle under a pseudonym for a year until things calmed down a bit (and the emperor became busy with a war against France).
Contrast Luther's experience with that of Jan Hus in the early 15th century. Hus, after making many of the same arguments Luther would a century later, was summoned to a church council (which had been convened in the hopes of ending the Western Schism, during which two, and later three, men all claimed the papacy). Hus was promised safe passage as well. Hus had been supported by his ruler, King Wenceslaus of Bohemia (also former king of Germany and emperor-elect, until he was deposed from that throne by the electors), but the council Hus traveled to was held in southern Germany. Wenceslaus had little influence there, and was unable to protect Hus. The safe passage promise was broken as soon as Hus arrived. When he refused to recant his teachings he was burned at the stake.
TL;DR: If you want to challenge the legitimacy of a traditional power center that has held sway for a thousand years, try to get your message to go viral, and have some powerful friends.