If the moon attracts the earth, why does the earth not move towards the moon?
Earth and moon is an example of a two-body system. They both rotate in an orbit such that the centripetal force required for circular motion is provided by the gravitational force.
Assume centripetal acceleration of earth to be $$a_e$$
This is a very small value, and hence the centripetal acceleration is very small. Also, the mass of the earth is very large and hence the center of mass of earth and moon system is very close to the earth. So, the radius of rotation of the earth is very small and negligible.