That's a bit like telling people who live in dangerous areas that the best response to a mugger is not to let them impoverish you. Bullies select people who seem physically or emotionally fragile to start with.
I have to agree with the sentiment expressed elsewhere in the thread, that bullies bully for different reasons. The only time I have been bullied, avoidance and not showing a response worked, because the bully had low self-esteem and was looking for acceptance from his peers by picking on smaller kids. When he saw that he wasn't getting anywhere with that, he stopped.