Say instead of just walking, the man was laying down a net/barricade around the tree. As soon as the man completes the circumference, the squirrel must admit that it has been gone around.

Now let us suppose the squirrel is at the same distance as the man.

Has the man have gone around the squirrel and the squirrel around the man?

If it's only radii less than the other, where is the limit?

To get it I think I have to re-frame it like this:

If you hold out an object toward the centre, you clearly go around it when completing an orbit.

If you keep extending that to the origin but then go beyond, so your arm is longer than the radius, then you still go around it, until your arm reaches twice the radius.