The fundamental error of the Holy Office was to elevate a scientific theory to a theological doctrine. Bellarmine was fortunately much wiser.
People forget that scientists came up with the Ptolomaic system—not theologians. The Fathers merely accepted the prevailing scientific theory and, to some extent, built a theology around it (cf. Dante).
As to why the Holy Office thought it was scientifically foolish and absurd, I’m not sure. Maybe because if the earth moved then there had to be a stellar parallax, and no one had ever been able to see one. Course we know now there is a parallax—it’s just too small to see with the technology they had available.
I think it was Galileo who elevated his theory to a theological certainty. All physical theories based on math were treated as hypothetical by Bellarmine and others. Paradoxically, today’s atomic physics are almost entirely a matter of mathematic rather than physical description.