Newton’s thirds law states that for every force, there is an equal and opposite reaction force. This occurs when someone is throwing the football and when someone is catching the football. When someone is thowing a football he/she is apply a force on the ball, so the ball apply the same force back to your hand. The reason why your hand doesn't snap back, it because we have muscles in our body  to counteract the force that the ball apply back on to me. Newton's third law also accurs when someone is catching the fooball. When someone is catching the ball  applies a force on to my hand and my hand apply the same amount of force back on to the ball, that's how I stop the ball from traveling any further.