Yeah, of course it's pretty bad. It's just a social no-no. In the OP's example, he reacted pretty much the way he's supposed to; without real violence. Pushing isn't nearly the same as, say, a sock in the face, and also I feel like being siblings changes things up a bit. Girls don't like the idea of getting punched (but then who would), and guys have an instinctual revulsion and violent reaction to that happening to girls. Even verbal insults that guys would shrug off, directed toward a girl, provokes that "white knight" mentality. I personally believe that abusive boyfriends and husbands are the scum of the damn Earth.
Let's put this in perspective, though: Snookie from the Jersey Shore? She was running her mouth, she was talking sh!t to a guy who was bigger, meaner and already had quite a few drinks in him. He was telling them to basically piss off and stop talking to him, but she just had to get her words in. She was surrounded by big dudes that like her (for some reason) and figured she could say whatever she wanted to anybody with no repercussions. She learned quick.
Now if one of those douchebag guys had been leaning over, talking sh!t to a stranger and yelling in his ear, even longtime watchers would have figured he deserved it. Snookie, though? She's got a vagina, therefore "that's not cool bro" and it's totally OK to then hunt down the guy. I'm not saying it's exactly the same thing, but it does make me think. Scum is scum, and bar fights are bar fights, regardless of the genders of the people involved.