Rotate means 'to move' or 'cause to move' in a circle around an axis (or spin as if on an axis).
When the moon first formed, it had a rate of rotation (spin) different than what we observe today. But, as one side became heavier than the other side, the side with the greater mass and gravitational attraction became "tidally locked" with its primary (Earth). Though the moon does rotate, it does not "spin" on its axis.
Why we always see the same side of the moon?
I say that there is 'active rotation' of most moons around planets and 'passive rotation' of others. Those that had energetically retained their inertia spinning motion from the early formation of the solar system are actively rotating. But our moon formed into a spherical lump by a different process and never had proper rotational motion embued in it. Others' spinning motions were disrupted by outside forces such as collisions.
At the 46 second mark in the first minute of the following video, note the swirling,spinning, rotational motion of the nebular cloud as it flattens itself into a spinning disc. Also, note the spinning mini-swirls that form into planets away from the sun. It is this active spinning that we see the rotation of planetary bodies today.
The Nebular Theory of Solar System Formation (3 minutes)
Real solar system forming right now:
Image of a solar system in early stage of formation: