Why don't satellites crash if gravity is attracting them towards the center of the earth?

Answer 1

Because they are in orbit which means they have enough forward motion to keep them into a state of "Free Fall". A satellite is falling to earth's center due to gravity. But for every inch it falls toward earth, earth move out of it's way by one inch.

Answer 2

Satellites orbit the Earth because they are moving fast enough horizontally that the gravitational force pulling them toward the Earth is balanced by the force causing them to move in a circular path around it. This results in a stable orbit where the satellite continuously falls towards the Earth but never hits it due to its forward motion.