If all motion is relative, then the geocentric model works, too. The math to calculation positions of planets is just more complicated I suppose. (Calculating such things is not my thing.)
Just because it's possible to work out the necessary math so that when you walk to your kitchen, actually the entire universe moves around you while you stay perfectly still, until your refrigerator presents itself to you and a jar of pickles jumps into your hand, doesn't mean it has any likelihood of being reality.
the math for orbits of other planets if the earth is the center of the solar system requires them doing infinite epicycles ((loop-de-loops)) and changing direction unpredictably, as though there are no physical laws at all.
but with the sun as the center, a few simple and elegant equations describe all motion with incredible precision.
kinda an Occam's razor argument, sure - but the worldview that allows you to actually understand things, act on them and make basic predictions is a lot more worthwhile to actually implement than one in which all is chaos and there is no order or consistency.
Isaac Newton was a devoted Christian. in his view, the existence of these elegant laws of motion and discernable, ubiquitous order in the universe was proof of it having been created by a logical, sentient God - far more proof than may kind being the center of all things, which is honestly just vain humanism.