[Junior]

Indeed, the Moon's core is not solid, and that is why it is tidally-locked. Good for you. However, your original statement:

The swinging weight of a molten moon core would either have sent the moon flinging off into space or would have sent it crashing to earth.

Is still not accurate. Several Jovian and Saturnian moons have molten cores (hence, vulcanism) and they have neither been sent "flinging off into space" or crashing into their primaries.

[WildTurkey]

Indeed, the Moon's core is not solid, and that is why it is tidally-locked. Good for you. However, your original statement:

No. I think his original statement had something to do with he could not understand why the moon didn't spin and now he has cut and paste from the site that I paraphrased my response to him from. He does know how to google.

[houeto]

Several Jovian and Saturnian moons have molten cores (hence, vulcanism) and they have neither been sent "flinging off into space" or crashing into their primaries.

That is why I think that an electromagnetic influence is underway. Gravity would not hold the moons in place.