Your geometry course "for me" does the following:

It is from a conflation graph, one whose purpose is to show axis location in the body, and total movement *of whatever kind*, relative to that axis. Drawn and thought of as a stationary body but accounting for non-stationary axial direction movements, yes, the Moon spins on its axis.


But if drawn to indicate not what the axis does over space, but what the body does relative to its axial forward momentum ... no, the Moon does not spin on its axis, properly speaking.


You are saying it doesn't rotate at a static point in space. What object does?



No object rotates at a static point in space; it is relations which define the distinction.

You may wish do obfuscate further, but in order to understand movements we always have to use geometrical distinctions.

Just as the Cartesian graph depicting, as if at one point, what the Moon's forward rotation (axis moving forward on a path) does to its overall orientation relative to the Earth-Moon barycentre ...

And a Cartesian graph showing if the Moon changes (spins) relative to its forward momentum (which it does not, and it would be shown static in such a graph ...

So too, does the issue of "static points" need definition.

In relation TO EACH OTHER (which was the big insight which drove Einstein), points can be defined as static, but there is no absolute set point (that we know of).

So, in relation to the Sun, Venus has spin AND angular momentum. Its Cartesian graphs would show orientation rotation (like the Moon) but would also show orientation relative to its momentum (unlike the Moon). How does this work?

The Sun is fixed relative to the orbit of Venus.

Now imagine Venus were not moving forward, as if it were a fixed point (which is how we make distinctions about proper motions, even if the real body is also in real life moving relative to something).
Would it still have spin on its proper axis? Yes.

The Moon, however, always faces its angular momentum, or path.

Imagine the path gone (and do a Cartesian graph of that, not the momentum angles as all of you have presented) and you would see no spin on the Moon's proper motion.

Or you could just look at it going forward, always facing the place it goes next.

Hence the distinction.
As you know, I assume ...