Phil Plait has an excellent summary of why Geocentrism is wrong over at Bad Astronomy, including this particularly insightful bit:
I never thought about it that way! Thanks, Phil!
Look, I’m human: I say "The Sun rose in the east today", and not "the rotation of the Earth relative to the rest of the Universe carried me around to a geometric vantage point where the horizon as seen from my location dropped below the Sun’s apparent position in space." To us, sitting here on the surface of a planet, geocentrism is a perfectly valid frame of reference. Heck, astronomers use it all the time to point our telescopes. We map the sky using a projected latitude and longitude, and we talk about things rising and setting. That’s not only natural, but a very easy way to do those sorts of things. In that case, thinking geocentrically makes sense.
However, as soon as you want to send a space probe to another planet, geocentrism becomes cumbersome. In that case, it’s far easier to use the Sun as the center of the Universe and measure the rotating and revolving Earth as just another planet. The math works out better, and in fact it makes more common sense.
However, this frame of reference, called heliocentrism, still is not the best frame for everything. Astronomers who study other galaxies use a galactic coordinate system based on our Milky Way galaxy, and the Sun is just another star inside it. Call it galactocentrism, if you want, and it’s just as useful as geo- or heliocentrism in its limited way. And none of those systems work if I want to know turn-by-turn directions while driving; in that case I use a carcentric system (specifically a Volvocentric one).
You use coordinate systems depending on what you need.
So really, there is no one true center to anything. I suppose you could say the Universe is polycentric, or more realistically acentric. You picks your frame of reference and you takes your chances....That’s where Geocentrism trips up. Note the upper case G there; I use that to distinguish it from little-g geocentrism, which is just another frame of reference among many. Capital-G Geocentrism is the belief that geocentrism is the only frame, the real one.