Then literally everything is orbiting literally everything else, and the word orbit is completely useless.

I have a gravitational effect on the earth. The earth-hperrin system has a gravitational center that both bodies revolve around. Does that mean the earth and I orbit that center? No, because my effect on the earth is negligible. The absolutely immeasurably small wobble my mass gives the earth is not an orbit. There are bodies much more massive than me that the earth orbits (despite how many Doritos I eat).

To put in less hyperbolic terms, Mars’ moon Phobos and Mars have a gravitational center, deep deep deep within the Martian core that both bodies revolve around. Does that mean Mars orbits this point? I don’t think a reasonable person would say so. A massive body wobbling because of a small body orbiting it is not orbiting. Only one thing in such a system is orbiting.