Also, the reality of climate change isn't a "point of view" any more than saying that "the earth orbits the sun" is a point of view.

So while it's true that you can work the equation from either reference frame defining each as orbiting the other, the center of mass will more than likely lie in or closer to one or the other, and with that you can define which is orbiting the other canonically.

Whereas "the sun and the planets all orbit the earth" has astonishingly little predictive power.

Not a geocentrist myself, but it did have good predictive power.

"To summarize, Ptolemy devised a system that was compatible with Aristotelian philosophy and managed to track actual observations and predict future movement mostly to within the limits of the next 1000 years of observations. The observed motions and his mechanisms for explaining them include:"[0]

Obviously not as good as current models, but it's a bit of historical rewriting to say that geocentrism wasn't a good model for the time, which is one part of why there was push back for heliocentrism. With the tools of the time, the heliocentric model had similar predictive power. Geocentrism at the time wasn't just about god, it actually had predictive power.

"He also argued that his system was more elegant than the traditional geocentric system. However, the predictive power of his model was not substantially better than its competition."[1]

[0] - https://en.wikipedia.org/wiki/Geocentric_model

[1] - http://astronomy.nmsu.edu/tharriso/ast105/Ast105week04.html

Had Jupiter's moons been visible to them, their motion would have confounded their model entirely.

Also, "The change from circular orbits to elliptical planetary paths dramatically improved the accuracy of celestial observations and predictions." Your own link says the predictive power was "dramatically improved."