Explain why an object moves if the action-reaction forces are equal.

An object moves even though the action-reaction forces are equal because not all objects have the same inertia, which is resistance to motion. This is why when you hit a ball with a bat the ball goes flying while the bat is only pushed back a bit. It is also why whenever you stand on earth, you're technically pushing the earth down a very small amount. You just can't notice it because the inertia of the earth is so great.