The Earth has a greater mass than you do. It certainly moves towards you, but much less than you do. This can be explained by Conservation of Momentum, or equivalently, by Newton's Second Laws and Newton's Third Law. (By the Second Law, Earth's force on you is the same as your force on the Earth. By the Third Law, the effect on a larger mass, of the same force, is less.)
Technically, as you jump up, the Earth is pushed down; as you come down, the Earth moves up (and meets you). But you weight little and the Earth weighs much more -- so don't expect to see any movement. Besides the Earth is less of a whole than you are. For instance, in a canoe, you jump out to the right. The canoe (and some water -- read "and some of the Earth") move to the left.
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