bullies feel better about themselves by picking on others.

I think he's right about some bullies, but not all. There are those who don't necessarily have a need to feel better about themselves, but have been conditioned to believe that this is the correct way to behave. That is to always assert yourself either physically or verbally, whatever helps you reach alpha status among your peers, in order to gain the respect of everyone around you. If you're the biggest & strongest kid on campus you can usually just pick on anyone your age at any time and probably achieve that. There are also those that don't really have any malice or need to feel better about themselves, but are apathetic in their eagerness to gain a mutual favor with others, and so they make fun of the same people that their friends are making fun of. There are still others who simply have a bone to pick with a certain type of person. Perhaps because of conditioning or revenge, or at times even over reason and rationale.

Self-loathing may be a reason to bully, but it's not the only one.