"Don't feed the troll" was actually a play on words that came second. Originally, online, in chat rooms and whatnot, "trolling" was what people did who just wanted to maliciously engage, as in this Merriam-Webster definition:
"to fish by trailing a lure or baited hook from a moving boat"
So you take the bait and argue, and they've hooked you, and will continue relentlessly to argue, because the point of the exercise from their standpoint is to start the argument and never let you win.
"Don't feed the troll" is just the next step, using a noun spelled the same as the verb "troll." You go from being baited to an ugly Norse fairy tale creature that lives under a bridge (or in a cave) and springs out to attack you.
(Note that trolling for fish is different than trawling, which involves pulling a net.)
Anyway I'm right because I was there when Al Gore invented the internet. :-)