My colleagues once spent a good hour trying to explain this fact to me and I still really struggle to accept it. I can see that the moon is rotating on its own axis from the point of view of a space that is external to the system it forms with the earth. But then isn’t everything on earth rotating about its own axis with respect to that external space? It seems arbitrary to isolate the moon from all this other stuff and make a special case of it…

1. Unlike position and velocity, which are relative (there is no given "origin" for them, no way to say where a thing is or how fast it's moving except relative to other things), rotation is absolute. A thing is either rotating or not, regardless of its relation to other things. Objects that rotate "experience (centrifugal) forces as a result" or "require (centripetal) forces to hold them together" depending on how you choose to describe it. This is detectable: hook two weights together with a newton-meter in space and the newton-meter will read non-zero when the assemblage is rotating, zero when not. The reading tells you how fast it is rotating regardless of any external reference point. (An equivalent device to detect position or velocity is not possible, but it is for acceleration.)

2. Yes, everything "at rest" on earth is in fact rotating at the rate the earth rotates. If you stand on the equator at midday and do not rotate you will be standing on your head at midnight.

> But then isn’t everything on earth rotating about its own axis with respect to that external space?

From the point of view of the moon, for the purposes of action due to gravity, anything on Earth is essentially part of the Earth, not an entity that is massive enough to be considered separately. The aggregate centre of mass is what counts. Similar for the Sun looking at the Earth/Moon system: from that PoV Earth+Moon is it a single mass with a centre somewhere between the two major masses that form it.

If the Moon where sufficiently consistent in its shape and density, it could rotate freely in any direction while orbiting the Earth, that fact that it is more dense on one side means that it is more energy efficient for it to spin in step with its orbit such that the dense side keeps facing us. If something massive hit the moon (let's assume this somehow happens without significantly affecting its orbit or causing significant problems for Earth too!) it might push the rotation off for a bit, but it would slowly be pulled back into sync. If something sufficiently massive simply landed on the moon, that would affect the mass distribution and the exact face that points at us would slowly change to reach a new equilibrium.

Pick the sun as reference: the moon rotates. Pick the earth as reference: the moon rotates. Stand on the moon and pick any star as reference: the moon rotates.

From which reference frame would it not rotate?