Same reason there are tides on Earth.
That same “pull” from the Moon which creates the tides on Earth also creates an pull on the Moon.
But the Earth is rotating faster than the Moon is orbiting. This makes the tidal bulge move ahead of the Moon at all times, which imparts a small but not insignificant increase in speed to the Moon’s orbit. (It also causes the Earth’s rotation to slow down in exchange)
And when an orbiting object increases it’s speed, it must also increase it’s altitude/distance.
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