This question concerning why 2 tides is probably the WORST answered question in physics. Most, if not all, introductory astronomy text books answer it incorrectly.
Most answer it as if the Earth-Moon system was stationary, just pulling at each other.
The Earth-Moon system rotate about one another in a gravitational dance. Since the earth is SO much more massive than the moon, they actually rotatate about a point INSIDE the earth, about a quarter the way down from the Earth's surface towards the Earth center.
So at the earth's surface closest to the Moon, BOTH the moon's gravitational pull AND the cenrifugal force are towards the moon. So there is a tide on that side.
At earth center, the centrefugal force exactly balances the gravitational attraction.
On the side of the Earth furthest from the moon, the Centrefugal force is greater than the gravitational attraction since it is almost twice as far from the center of rotation as it needs to be, so it wins, and there is a ttide there only.
The earth moon system needs to be seen as a pair rotating about one another to understand this 2 tide phenomenon.