Question

If, according to Newton’s third law, every reaction has an equal and opposite reaction, then how can motion ever occur? Wouldn’t every force be canceled out by its reaction force?

Answer 1

Motion could not occur if the action force and the reaction force

both acted on the SAME OBJECT.

But they don't. They act on different objects.

The pusher applies the action force to the thing he's pushing, and

the thing he's pushing applies the reaction force to the pusher.

Newton never said that equal and opposite forces cancel out

when they act on two different objects. Only when they act on

the same object.

Answer 2

No, if you push an object, the other side is also "pulling it".

Motion occurs because of the equal and opposite reaction.