food for thought...not that this proves the earth is flat...
what a perfect coincidence that the moon and the earth rotate at an exact rate each (different rates as they are different sizes) for us to always see the same side of the moon...
That's not why you see the same side of the moon. It is because the rotation of the moon is the same rate as the time it takes for it to orbit the earth once, that phenomenon is called 'tidal lock' and has been observed in other parts of our solar system. The moon is tidally locked to earth but the earth is not tidally locked to the moon, if it was then the moon would never move from our point of view.