I could point you to countless scientific discussions which point out that geocentric modeling is a perfectly valid and useful model, which is quite different than believing the earth is the center of the universe, which I never said. It is a perfectly valid frame of reference.
The only test that ultimately counts for whether a particular theory is true is whether it makes accurate predictions.
Geocentric theories can make accurate predictions about planetary motion. In this sense, they can't be said to be false.
But geocentric theories of planetary motion are highly complicated and convoluted compared to heliocentric theories, so heliocentric theories are generally preferred. Heliocentric theories also have the advantage of being consistent with the rest of physics (not just planetary motion), while geocentric theories would be harder to incorporate into standard theories of force and acceleration and whatnot.
You say, for example, that the earth is a perfectly valid frame of reference. But in Einstein's relativity, frames of reference are used to measure velocity -- not acceleration. The earth and sun revolve around each other, and revolution is acceleration. We can say that I am moving with respect to Cleveland, or that Cleveland is moving with respect to me, or that we are both moving with respect to Jupiter. But we do not say that I am accelerating with respect to Cleveland. Either I am accelerating or I am not -- there's no "with respect to" about it.
Since revolution involves acceleration, it is not just as valid to say that X is revolving round Y as it is to say that Y is revolving around X. In the case of the sun and the earth, they are both revolving, but the earth's revolution objectively involves more acceleration than the sun's. In that sense, the earth revolves around the sun a lot more than the sun revolves around the earth -- irrespective of any frame of reference.