What seems to be happening in the Foobiverse is that people don't creep on weak people who can't hit back because they're weak people who can't hit back; they have to have a stupid excuse because that's how things work in the Foobiverse. What seems to be happening in Brad's case is that he sees himself as being the victim of a rich snot who gets treated like his spit tastes better than everyone else's while he has to deal with a stereotype whining, cowardly, abusive drunkard who pisses his life away at bars because that's what Mother Ridgway says that poor people do. In Mike's case, he assumes that Lizzie has the world on a string while his life is one of bleakness and despair and his parents not wanting him around. In both cases, we're dealing with two kids who aren't even close to having an accurate picture of the life of the person they're being a shit to. For the longest time, Brad had no more idea that Mike got treated like something that John scraped off his shoe than Mike does that Liz feels as if she can never catch up to her whining imbecile of a brother.
The difference between Brad and Mike is thus quite simple: Bradley Luggsworth is not some idiot of a Patterson suffering from a terminal case of fecal encephalopathy. At some point, he seems to have realized that Mike had a shittier home life than he did and started feeling almost sorry for him. The keen observer of the human condition providing for his family with his miracle typing fingers still doesn't see that Liz lives a life of quiet desperation in which she can never be quite good enough as he is. This is because he isn't a bully beating up on a weaker child out of spite, malice and envy. She has to have done something to deserve it because television says so.