Why does only one side of the Moon face the Earth?
Synchronized rotations would not last so long. There must be some force holding this pattern in place. Could it be that the center of gravity of the Moon is not in the middle of the Moon?
One side of the Moon always faces the Earth because the spinning period of the Moon is the same as the time it takes for the Moon to orbit around the Earth. This is called tidal locking. This demo on Wikipedia shows how it happens very nicely:
Yes, there is a force that’s holding the Earth and the Moon in this configuration, and it is simply the gravitational force between the Earth and the Moon.
We know that tides here on Earth are caused by dragging of the Moon. In the reverse, the Earth is also dragging the Moon with its gravity, creating bulges on two sides of the Moon. If the Moon does not rotate and revolve at the same period, then the bulges will no longer point directly to and against the Earth. The gravitation force on the two bulges will then become uneven and create a torque to rotate the same side of the Moon back to the Earth. The “locked” phase is the most stable geometry for the Earth-Moon system. Just like rolling a ball in a valley, even the ball starts to be on a hill, it will be dragged to the bottom of the valley eventually by gravity.
This kind of tidal locking is not uncommon in the Solar System. For example, Pluto and its moon Charon are locked in a very close orbit.