There've been several good threads about Galileo in the past; here's one that seems on-point.

In short, the Church weren't offended by his scientific proposals - Copernicus had published his theory earlier without any problem - so much as by his strident insistence that Copernicus was right while completely ignoring counterevidence such as the absence of stellar parallax. (The parallax actually does exist; it's just too small to see with the naked eye because the stars are much farther away than anyone thought at the time.) What finally sunk his case was that he insulted the Pope in print while ignoring prior ecclesiastical court orders.