Question

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

Answer 1

The question cannot be valid, because if action-reaction forces are equal the object will not move.

Answer 2

Newtons third law says that Every Action has equal and opposite reaction. But that does not means that object not move if action and reaction are equal. That is because Action and reaction occcurs on different body not on same body. Let me show this with a diagram