and to say that this deep into the thread is just sad
If you think of a binary star system, you see that the two stars "revolve around each other". The masses of the two stars create a point in which both the stars are gravitationally bound together, called a Langrangian point.
The same is true for our sun and the planets, the earth doesn't revolve around the sun per se, it (along with the sun) revolve around the Langrangian point created by both masses.
So if people say that binary stars revolve around each other because they revolve around a mutual Langrangian point than the same could be said for the sun and the Earth. So in that case, if x is revolving around y, then y also has to be revolving around x because there is always a Langrangian point.
Another example, the moon revolves around the Earth, so in that case the Earth also revolves around the moon because we share a Langrangian point.