Remember that the Earth is pulled toward the moon as well. The water facing the moon is closest to it and thus pulled toward the moon **more strongly** than the Earth is, making it go away from Earth, and the water opposite the moon is farthest from it and thus pulled toward the moon **less strongly** than the Earth is, again making it go away from Earth.
[More detail](https://www.youtube.com/watch?v=bPhhYhN0FAc)
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