If the moon attracts the earth, why does the earth not move towards the moon?

The Earth and the moon experience equal gravitational forces from each other. However, the mass of the Earth is much larger than the mass of the moon. Hence, it accelerates at a rate lesser than the acceleration rate of the moon towards the Earth. For this reason, the Earth does not move towards the moon. 

The earth does not move towards the moon inspite of the attraction by moon because the force with which moon attracts the earth is same by which earth attracts the moon. So net force on the system becomes zero.

The force exerted by the earth and the moon on each other is insufficient to move the earth, on account of its huge mass.

the Earth and the moon experience equal gravitational forces from each other However , the mass of the Earth is much larger than the mass of the moon, Hence , it accelerates at a rate lesser than the acceleration rate of the moon towards the Earth ,For this reason , the does not move towards the moon .

The moon attracts the earth with the same force as earth attracts the moon. The force of attraction of earth on moon provides the centripetal force required by the moon to relolve around the earth. Infact, earth is too heavy to move towards the moon, under the action of the same force force.

The force exerted by the earth on moon is used in used changing the path of moon from straight line to circular path. The moon attracts the earth with the same force. But the earth is too heavy to move towards the moon. Rather, we can show that distance moved by earth towards the moon is so small that it cannot be detected.