This is because the Sun also exerts a tide. The size of tides also depends on the Earth-Moon distance. When the Moon is closer, the tide is larger. The solid Earth experiences a tide as well. The amplitude is up to 10cm.
Tides also transfer spin from the Earth to the Moon.
The Earth is slowing down and the Moon is getting further away. Phobos is doing this. When there are several large satellites in a system, lots of oddball things can happen. The tidal interaction between Jupiters four large moons causes Io's volcanoes. The Sun also exerts tides on other planets.