[false-mirror]

You're referring to the fictitious centrifugal force [0] which is actually a minor change in inertia—very much out shined by the centripetal force of gravity. For example, on earth if you weigh 200 lbs on the North Pole, you'd weigh about 199lbs on the equator. On the moon, this tiny effect would be wiped out by gravity.

[0]:https://en.wikipedia.org/wiki/Centrifugal_force

[OscarCunningham]

Your example with the North Pole refers to the centrifugal force from the Earth spinning on its axis. But the relevant centrifugal force here is not the one from the Moon spinning on its axis, but rather the one from the Moon orbiting the Earth.

But in any case, you can think about the whole thing without considering centrifugal force. If the Moon wasn't orbiting but rather in freefall towards us, then the Earth would continue to have two tides right up until the moment it hit us.

The point is simply that gravity weakens with distance. So the pull of the Earth on the near side of the Moon is slightly stronger than the pull of the Earth on the Moon's centre. And the Earth's pull on the far side of the Moon is slightly weaker than the pull of the Earth on the Moon's centre. So if we consider the near and far regions of the Moon relative to whatever the Moon is doing on net, it will be as though the near side is being pulled towards the Earth and the far side is being pushed away.