I don't know how to explain it, but I'd almost rather the flag options be worded as "Sorry, this comment seems: uncivil" or "Sorry, this comment seems: off-topic" to lighten it a bit. If they were a friend in real life, I'd take them aside and say "hey man, that comment was great, but you might want to soften the tone. It kind of came across as rude."
Downvotes end up being seen as judgments of your ideas, and I would love to be able to provide better feedback. This would be great if this could somehow give the user a nudge that they wouldn't feel defensive about.
It may seem like a minor point, but I feel a little guidance would go a long way in helping users get the sort of social cues they already get in a real-life conversation.
Edit: Instead of calling it out as flagging, I'd be okay with a downvote system that simply/optionally let you specify a reason to provide (with 3-4 common nicely-worded options). I don't care about upvote reasons at all.