Question

When a force acting on a body has an equal and opposite reaction then why should the body move at all

Answer 1

According to Newton's third law every body gives an equal and opposite reaction. this is true. but when force from one side increases than the body moves along in the direction of force.
hope this is helpful!

Answer 2

The body moves when there is an opposite reaction by another body due to the force that acts on it. An object can move if there is an unbalanced force acting on it.