The moon does not affect bodies of water. The moon's gravity pulls every mass equally. The water being closest to the moon is pulled more strongly than the earth whose center is 6300 KM away from that water - so the water creeps closer to the moon than does the center of the earth.
Same thing on the other side - the water is 6300 KM further away from the moon than is the (center of) the earth. So it is pulled less strongly, and thus to an observer on the earth it looks like that water is being pulled away.
"The moon does not affect bodies of water. [description of how bodies of water are affected by the moon]" lmao fucking nerds, man.
So, hypothetically, if our blood or CSF had a different mass-slash-density than our bones, and our skulls were further from the earth's surface than the rest of our bodies, they could conceivably be pulled more-or-less strongly than the rest of it?
It actually does not depend on the density, because mass is on both sides of the equation. Your head is in fact pulled on less than your feet. For an extreme example, look up "spaghettification".
Same thing on the other side - the water is 6300 KM further away from the moon than is the (center of) the earth. So it is pulled less strongly, and thus to an observer on the earth it looks like that water is being pulled away.