I think if you experience bullying as part of your formative social experiences you can absorb it as sort of "normal" and assume it is part of how the world/social interaction works, and following that logic through - if the whole world did work on a basis of bullying, then the only way to get ahead would be to be the bully, rather than the victim. So I think it does sometimes happen as a sort of defense mechanism, if that makes sense, and particularly if a child doesn't have many skills in other social areas, so doesn't know how to make friends or interact with people or avoid being a victim in other ways, then they might default to bullying as something that they know "works" whether that means that people leave them alone because someone else has become the target, or are seen as someone not to be messed with, or whether they gain power/control/status over other children.
Not all bullied children become bullies, but IME when a child keeps using a dysfunctional or antisocial approach it's often because they lack realistic alternatives, or believe that they do because of their experiences to date.
There does seem to be a small number of people who seek power for the pure pleasure of it, and such people often seem to have been that way since they were very young, but most of the time children seeming to seek power and control are doing this as a sort of defensive thing because their experience has taught them that unless they assert their power in this way, they will have none at all. They don't have the positive experience of an environment where autonomy, equality and safety are ensured without that power struggle.