I don't see how that's an apt analogy. Geocentrism put the Earth at the center of the universe, around which the rest of the universe rotated. But saying life on Earth originated on Earth does not in any way put the Earth at the center of anything. Nor does it in any way mean that Earth is unique.
The bottom line is that -- because we don't know how abiogenesis occurred, whether here or somewhere else -- we have no way to judge how common it is. It could be that, given enough time, life spontaneously forms on any planet or moon that offers a certain set of conditions, and Earth just happens to be one of those planets, meaning it is still not "the center" of anything.
In fact, in the extreme case, panspermia is much more geocentric, saying that life formed in just one very special place -- maybe not the Earth, but somewhere, the "center of life in the universe" -- and then spread by diffusion to all the other locations in which life existed. But that seems like an unlikely and unnecessary model; if life can spontaneously begin somewhere, why should we assume it can't begin in many places, and if that's true, why not also on Earth?
The bottom line is that -- because we don't know how abiogenesis occurred, whether here or somewhere else -- we have no way to judge how common it is. It could be that, given enough time, life spontaneously forms on any planet or moon that offers a certain set of conditions, and Earth just happens to be one of those planets, meaning it is still not "the center" of anything.
In fact, in the extreme case, panspermia is much more geocentric, saying that life formed in just one very special place -- maybe not the Earth, but somewhere, the "center of life in the universe" -- and then spread by diffusion to all the other locations in which life existed. But that seems like an unlikely and unnecessary model; if life can spontaneously begin somewhere, why should we assume it can't begin in many places, and if that's true, why not also on Earth?