I have to agree on that. I've seen people take the mildest statements possible as "flames". For example: "I think the story you wrote was interesting, but sometimes you switch tenses in the middle of a sentence. The story would be more enjoyable if you corrected that mistake". That's not a goddamn flame. That's constructive criticism, pointing out something that's seriously wrong with a piece of writing. A flame (a mild and kinda stupid one, at that, at least for my standards) would be something like "Your story sucks, idiot. You deserve to die for what you did to the characters."
I guess nowadays people just aren't used to criticism, to being told they could be wrong. Replying to other people with anything else but nice comments is considered something you should not do.

To expand a little on the subject of discussion, I think there are different kinds of flames:
- dumb flames (like "OMG YOU SUCK YOU MUST DIE!!!!!!!!!111111111"), which come either from boredom or from utter stupidity and are easily disregarded by people who are in possession of that increasingly rare organ called a brain.
(I also consider "dumb flames" those written by those people who disregard all warnings and choose to, say, read a yaoi fanfic even if they're homophobic, and then flame the author for writing about gays. I don't care if those flames are well-written. Warnings were there, you ignored them, you have no right to flame.)
- normal flames, the ones with some thought behind them.
- awesome flames, the ones that manage to drive the point home better than any "calm" discussion would have. The ones that give the word "insulting" a whole new meaning, the ones that make you say "oh wow, I wish I could flame like that". An example? This one. I've seen it in many variations, short or long, with or without the postscriptum, and I have no idea who came up with that, but damn, I wish I could do something like that.

(For those who saw the first incarnation of this post... told you I would edit it. ;)