Why did many German rulers support Luther's religious movement against the Catholic Church?
Although different "princes" might have had different reasons (some might have truly believed Luther's message), most historians say that many of the rulers accepted Luther's message because they thought it would help them economically and politically.
In Luther's day, the princes of the various German state were in competition with the Holy Roman Emperor for control of their lands. They were technically subordinate to him but they did not exactly want to just give in to everything he said. Because of this, the idea of a new religious movement appealed to them.
Luther said that there should not be a church that was ruled by a pope and a central organization. He thought that each state ought to control its own church. You can see where this would sound good to the princes. If Luther's ideas spread, the princes would be able to take over Church property and they would be able to have a lot of control over the church in their state.
In this way, Luther's ideas sounded beneficial to the princes both economically and politically. This is why they supported those ideas.