To make this argument, we must look at the the nature of these two sorts of crimes. We can say that web sites should control pirated material and not bullying because it is relatively easy to objectively determine what material is pirated while it is very difficult to objectively define bullying.
Pirated material is pretty easy to spot. Any website that is hosting torrent files of popular music or movies or TV shows is clearly hosting pirated material. There is no subjectivity to this judgement. But bullying is much less easily spotted. If I go on Facebook and I post "You suck" in a comment on a friend's status, how is Facebook supposed to know whether I am bullying that person or whether I am joking? It would be incredibly intrusive and subjective if Facebook were to decide which of my posts were examples of bullying.
Piracy is objective and easily spotted. Bullying is not. Therefore, sites should control piracy but should not try to control bullying (other than giving people the option to block other people the way Facebook does).