Newton's third law: if action equals reaction, how does anything ever move?

This is the most common confusion with the third law. The key point is that the action and reaction forces act on two different objects, not on the same one. Forces only cancel when they act on the same body. When you push a wall, you push on the wall and the wall pushes back on you, but those two forces are on different things, so neither cancels the other. Take walking: your foot pushes the ground backward (action) and the ground pushes your foot forward (reaction). The forward push from the ground acts on you, so you accelerate forward. Motion happens because the net force on a single object decides its acceleration, and the reaction force is on the other object entirely.