In many ways I think Luther's problem was just how seriously he took Christianity. To understand him you need to look at the history of the Church for the last couple of centuries. This was the period when there were several popes, when a Council had to step in and save the Church. That started a continuing struggle between the authority of popes and councils. Many good people believed that in refusing to call a new council, the Pope was no longer really legitimate. It was also period of nationalism, where there was a lot of tension between the papacy and national governments.
The point is that there was lots turmoil. There was widespread cynicism about the Church. Many well-known Renaissance scholars were like Erasmus: skeptical about the Church but unwilling to do much about it. Luther, however, felt that people's souls were at risk, and couldn't sit by and watch while people he was pastorally responsible for were being abused.
It was also pretty much a low point for the papacy. The popes were in many ways more renaissance princes that Christian leaders. My read is that the Pope never really understood Luther's mindset.
You also shouldn't focus too much on Luther. The kinds of things he said had been said by many for quite some time. In the 95 theses, you can see pretty clear influences from Hus and others like that. I claim that what was different wasn't Luther but his prince. What was different about the Lutheran Reformation was that there was a prince willing to follow Luther's lead, even when it led to a break with the Catholic Church.
From everything I can tell, this wasn't just a political judgement, although it was certainly a period when many in Germany wanted to assert German independence, just as the background to Calvin was Swiss city-states that wanted independence of the conglomerate of bishops who were really princes, and the feudal overlords they worked with. But the Elector took Christianity very seriously. He was convinced that changes needed to be made, and was willing to follow through on it.
In my opinion the Pope simply wasn't up to leading the Church through a very tough period of time. He miscalculated, and precipitated the break. I believe he thought he could get Luther killed, just as church leaders had done with heretics in the past. But the situation had changed in ways he didn't understand.
In my opinion the Church is still trying to figure out how to handle a situation in which it no longer has secular power. How do you maintain unity in a situation where you can't persecute heretics?