If you step outside and watch the stars, and map them, you'd also come to the conclusion of a geocentric universe yourself. The nature of the sky makes it appear that everything is regularly revolving around us. And incidentally you can even create astronomical predictions based upon this assumption that are highly accurate. You end up needing to assume epicycle upon epicycle, but Galileo's theory was no better there since the same is true when you assume circular orbits.

So what made Galileo decide otherwise was not any particular flaw with geocentricism, but rather he thought that he'd discovered that the tides of the ocean were caused by the Sun. That is incorrect and also led to false predictions (like places only having one high tide), so the basis for his theory was incorrect, as were many assumptions made around it. But it was still interesting and worth debating. Had he treated 'the other side' with dignity and respect, it's entirely possible that we would have adopted a heliocentric view far faster than we ultimately did.