We haven't talked about this much in class, but being the history nerd that I am, I keep getting stuck on this point. The Church was under so much attack and looked so bad at this point in history (due to the Great Schism, the Reformation, the religious wars, etc) those in power were willing to take drastic measures to preserve what little power they still maintained. The Medieval mindset was one of repetition. No one expected change; life was very cyclical for almost 1000 years. The Church controlled everything, even how people thought, and no one ever considered challenging this way of life. However, as the Petrarch led the revolution in Italy towards Humanism, certain people in society began to embrace change. Reading the rediscovering, and translating for themselves, ancient texts by Greek and Roman philosophers, these forward thinkers began to realize it was "ok" to challenge authority. The process began in the 14th century and by the 17th century (when Galileo lived) it was still in its infancy. People were, however, now making some attempts to explore their worlds, make their own observations, draw their own conclusions, and challenge the current doctrine and truths.
This "thinking revolution" posed a great threat to the Church. They had controlled everything for so many years, they did not know how to handle such change. It has been a pattern through out history, who ever is in power wants to do whatever it takes to ensure they remain in power. This is not an outrageous claim, but in doing so, the Church prevented itself from incorporating scientific discoveries and other revelations into its doctrine. The actual discoveries made by someone like Galileo or Newton did not threaten the power of the Church, they could have been easily assimilated into the belief system. But, because the Church was so afraid of losing power, this was not an option. Thus, the Scientific Revolution, and later the Enlightenment, bloomed as oppositions to the Church, rather than as physical and philosophical support for the Church.
I'm not really sure where I was going with this post, or why I ended up where I did. But these were some thought that have been going on in my mind during our classes recently and I just felt like writing them down. Sorry for the "stream of consciousness" writing.