"Some people say light is waves, and some say it's particles, so I bet light is some in-between thing that's both wave and particle depending on how you look at it. Am I right?" "YES, BUT YOU SHOULDN'T BE!"
It's called a barycenter, kids, a common center that both objects circle around. That common center happens to be inside the sun, but that's a topic for next week's class in this semester's AP Astrophysics program.
I mean, no, not really. The gravitational center of the sun-earth system is within the sun itself, so the earth definitely orbits the sun and the sun definitely does not orbit the earth. Let alone the fact that the sun’s movement is predominantly driven by Jupiter. (The gravitational center of the sun-Jupiter system is just above the sun’s surface.)
As a middle ground kind of guy, I would like to pre-emptively state that a lot of us don't actually think the answer is always the middle ground between two stances. It's just that we're more likely to propose a middle ground solution because we evaluate the plausibility of both stances in a more balanced way (as opposed to existing-stance-holders who are prone to bias towards their own stance.) When the two seem roughly equal in plausibility (which happens fairly often, otherwise the argument would be more one-sided,) that's an indication to evaluate the middle ground as well.
Middle ground folks are often caricaturized as wanting to find the middle ground between an objectively sensible point A and a radically wrong point B, when the spectrum of opinions is sort of like [ - - - - - A - | - - - - - - B ]. In that caricature, we're looking for a middle ground at point C [ - - - - - A - | - - C - - - B ], when in actuality we're evaluating (and not automatically accepting) something two or three steps closer to A. In some such cases, A might already be the most sensible middle ground.