I have not had a mean rooster, what I thought was 'rough on the girls' was just how they mate! So, take my contribution with a grain of salt.
Some roo's I think are just bad natured, especially when they start thinking about girls and their protective instincts take over. Some traits I have read about kind of make sense to me. These are not human pets, they are flock birds with a strict hierarchy. Ideally, the owners want to be at the top of that, and not challenged by the flock.
In nature, the rooster rules the roost (and if he does not he is eventually killed or chased off) If this instinct is strong, he will challenge the owners (same as a dog). There are certain behaviors that we presume are nice pet friendly traits, but in the rooster world, those traits are being submissive. I learnt this with a alpha pullet who seemed to like to climb on our back when we bent down to pat another bird. We like to pat our nice birds, but to them, the alpha is preened by the lower level flock members. Patting and stroking is preening, and submissive. Holding them up high elevates him above the flock, bringing him up to your level, he thinks he is above you or at least in with a chance to be above you, so he will challenge.
They are just a couple of actions that we now don't do unless we have to, particularly with roosters, we need to keep them top of the girls, but below us, if they don't tow the line, they will soon be off to freezer camp. Similar to dog training, letting a dog walk over you makes them the boss IMO you need to keep that in check or you could face issues down the track.