Except unlike popular belief the church was very much involved with science. You see the church didn't actually believe that science was heresy but as a method to get closer to God by understanding the world he created.
But of course when you're been practicing science for a long time you centralize just like scientists do today. And you might ban certain sciences you deem offensive to your tastes just like scientists do now.>If they thought that Tycho Brahe were right they should've let them have public dispute and let people to decide but they just used political power to shut down opinion
Which was what the Pope was doing, you see quashing political dissent especially when the evidence were pouring in that he was right isn't a smart decision.
The pope sought out Galileo and they had many discussions, The pope would give his theory, Galileo would respectfully disprove them. All this was building up to a debate.
Because you see the church isn't a hivemind but one filled with many different people practicing different philosophies and unfortunately a good majority of them didn't agree with Galileo some because he was overturning doctrines that were now being proved false, others because he was flatout wrong.
Now the most radical of these priests wanted Galileo dead.
The Pope was not among that number he made a suggestion that in his next book that Galileo try to find a middle ground give evidence that he's right but also add in some pro geo centrism talking points so that he could diffuse the tension between the more radical clergy members.
Instead what Galileo did was right a book insulting the Pope, so now Galileo had insulted one of the people backing and protecting him. The Clergy members that hated Galileo used this to sway the pope over to their said>do you really want to protect a man that attacks you
What followed after was extremely predictable.