Can someone please explain why the moon and earths rotation are synchronized? Is it possible that it could become out of sync over time? I’m also confused at how it seems impossible that they would match up forever or even in the first place?
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What you are referring to is called “tidal locking” and the name hints at the reason it occurs.
When the moon was first formed it is theorized it started out as formed mostly from material from Earth blasted free by some immense impact. This glob of molten material would have been spinning wildly but being deformed by Earth’s gravity, stretching it out of a perfect sphere by the pull of gravity. This bulging would have shifted across the surface as the moon spun, but somewhat lagging behind as such shifts took time. Since this would lead to the bulge being unbalanced the pull of gravity would cause the spin to gradually slow, and the orbit of the moon to slow and become more distant from Earth.
Even today the moon is dragging our oceans around the world in a tidal bulge which saps energy from the moon’s orbit causing it to slowly move away from Earth. The moon becomes about 3.78 centimeters more distant from Earth every year.
So to answer your questions more succinctly, the rotation of Earth and the Moon are synchronized due to them pulling on each other via gravity. This tidal locking happens in other cases across our solar system and presumably the universe as well. They will not become out of sync unless there is some outside interference such as a massive body impacting their surface to impart a spin, but even if that occurred the process of tidal locking would just begin again.
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