"When a rifle shoots a bullet, Newton's Third Law says that the force that the rifle exerts on the bullet is exactly the same size as the force that the bullet exerts on the rifle - yet the bullet gets a much greater acceleration than the rifle. How can this be?"
It is absolutely true that the forces on the rifle and on the bullet are exactly the same size. However, don't forget that Newton's Second Law says that two factors affect the acceleration of an object - the net force on it and its mass (inertia).
The acceleration of the bullet equals the force that the rifle exerts on it divided by the mass of the bullet.
The acceleration of the rifle equals the force that the bullet exerts on the rifle divided by the mass of the rifle.
The two forces are equal, but since the mass of the rifle is much greater than the mass of the bullet, the acceleration of the rifle is much less than the bullet's acceleration.