Humans are not pure carnivore such as a lion/tiger etc. Our teeth are not designed to just bite and tear flesh. If you just open up and clamp your mouth on something, you may cause pain but you are not going to get much panic reaction from it. The purpose of biting is to cause panic in the other person and their instinct is to just get away. The time I was bitten in a fight, the person didn't know what they were doing and just clamped on and down, and it didn't even break the skin. Just an annoyance and made me want to hurt them more.
http://www.youtube.com/watch?v=vL24yv5bJaA&feature=plcp