Paul Fidalgo reminds us in a post at Near Earth Object that there is more to bullying than the simple dichotomy of being either a bully or a victim. Sometimes people caught in the middle between bullies and people that are more socially vulnerable find themselves battling on two fronts.
I had never even thought about this [both bully and victim] as a category, but it makes a lot of sense as I think back to those ugly days. Imagine: In desperation to avoid being bullied, or to make up for it in the eyes of your peers or in your own sense of self, you yourself turn to bullying someone else. In other words, since you find yourself unable to punch up, you opt to punch down.
Neither had I, though when I look back I suspect I fit into that category more than I would like to admit. Bullying is a difficult problem to say the least. It is often presented as an either/or situation with everyone wanting to eliminate the problem. Studies like the one Paul Fidalgo points out at Time should serve to let us know that it isn't that simple of a problem or it might have been solved long ago.
Regardless of how difficult the problem is, the least we can do is recognize bullying when we see it both in ourselves and in others. Even those of us that were bullied aren't immune from making someone else's life miserable. If we can be honest with ourselves and others, that might go a long ways in minimizing the amount of bullying that people have to face.