Chi Sao will teach you how to use both sides of your brain. The right side of your brain controls the left side of your body and the left side controls the right side. You will learn how to use both arms interdependently. A pianist can play one rhythm/melody with the left hand and another with the right hand. Try rubbing your head with one hand and patting you stomach with the other and vice versa. Now try doing it faster and faster as in a real fight. Get the idea?
Sometimes you can block and strike on the centerline. Sometimes you block on the centerline but strike along the central line.