Tim’s an old one, actually. Back in the old internet forum days, flaming was the act of going off on someone during an argument. Most forums even had “no flaming” rules, that could result in warns or outright bans if a mod thought an argument had gotten out of hand.

To be clear, flaming is the act of insulting the user, not the act of arguing against them. You can argue against a user without attacking the user directly.