Jesus is proclaiming Himself as this One, the One who is going to heal souls from sin, who will give power to overcome. Yes, He crushed the head of the serpent, but now He is turning around and He is giving us that same power to continue trampling over the rest of the body. He healed physical diseases and sicknesses and infirmities, but His greatest healing is still happening every day, in that we are being healed from sin.