So if for every action, there is an equal and opposite reaction, why does anything move?
If a horse is hooked up to a cart and the horse moves, why doesn’t the equal and opposite reaction of the pull of the cart counteract the pull of the horse and keep the two of them immobile?
Because the action and reaction are not the cart and the horse. They are the net of the horse and the ground and the cart and the ground and friction and the cart and the horse and just about everything else you can think of. Perhaps a bit more scientific, but you get the point.
So the horse moves the cart because of a state of disequilibrium, just as Newton stated in his other laws.