To avoid bullying it is suggested not to show anger to bully. Again also suggest to be assertive. Why?

When a person shows anger, that proves something has "gotten" to that person. A bully WANTS to "get" to their victim. Bullies are known for being easily hurt, and that is often why they put up a show of power. Someone they can make angry actually gives a bully the perfect person to pick on. It shows the power the bully has over the angry person.

But if a person acts assertive around a bully -- assertive, but calm -- the bully will not want to take on that person, because they will feel afraid of them.

So if a person gets angry around a bully, the bully instantly knows that the angry person is not strong, and will make an easy victim. But if a person acts assertive (without getting emotional) around a bully, the bully will find an easier target.

Bullies escalate sometimes into more hideous violence.
It also causes the bullied to become aggressive like the bully him/herself and why be a jerk just because someone else is?

You have to be assertive to let them know you won't tolerate the bullying but it is a fine line between assertion and aggression.

I hope whatever you are going through- that you can find someone in the counseling dept at your school or in human resources at work to talk to about it. Let someone else know what is going on.

Try to avoid the bully if you can and every morning use visualization techniques to picture them leaving you alone or even being kinder to you and to others. Approach them with kindness if you feel you can do so safely.
Get a copy of the Secret DVD from your library or buy it and you'll see what I mean. Go to thesecret.tv and check it out.

its shows that the person being bullied is better than the bully not to go to his level.. also not giving any agression back makes the person a better person. it also doesnt give the bully something else to react on and keep going

Bullies like it when you react. When you don't. It pisses em off! When you kick their ***, it's even better!