The laws of motion are the same in every reference frame, which means that statements like "X revolves around Y and not vice versa" are not "physically real" in the same way as "X and Y attract each other gravitationally" is, because they select one reference frame as privileged.
Rotating around a point still applies in any frame of reference. Spin a top and the axes of rotation is independent of your frame of reference. Pick an atom on that top and it’s rotating around a specific point in any frame of reference.
This goes back to the ambiguity of the definition of orbit. If I have a system with two points involved in some sort of rotational motion, then there isn't a "best choice" for which point should be considered the origin of my coordinate system.
If you mean exactly 2 abstract points in Euclidean geometry then sure. 3D objects are not points which is the first issue. Relatively also cares about accelerating or rotating reference frames which applies to both point masses.
The center of mass in a two body system is a nice inertial reference frame which simplifies calculations.
