I think in a way it IS to make them feel better about themselves. You see... You mentioned that they're usually "superior" in some way according to the standards of a given society. And they use bullying to assert their authority over lesser people. Thus it boils down to them doing it simply to validate in their mind that they are, in fact, superior in the eyes of their society. It's insecurity.
Also, I'm not sure if you actually "firmly concur" as you kind of said the opposite of what I said (unless I misread your post).