In short: the troll does not (necessarily) seek the reaction of the person they troll, but rather to create a ball of hatred and resentment that will drag everyone participating in their toxic debates. A true chain reaction to infect all those who are part of their macabre plan with their contempt for humanity. Don't let yourself be corrupted by the troll's machinations! Here's how!
Season 20 of South Park is a gem. Broadly speaking, it deals with the US presidential race, with the subsequent victory of Trump (played by Mr. Garrison), as well as the virtual war between the "politically correct" and the usual trolls, who just want to watch the world burn. I don't want to spoil the story if you haven't seen it, so we'll go straight to one of the standout segments of episode 10 (titled The End of Serialization as We Know It): The Axiom of Trevor, detailed below.
"The Axiom of Trevor is a well-known online trolling equation. It's a way in which a single person can create a massive reaction on the Internet. It works like this: person A trolls person B. But it's not about person B. The troll is trying to push buttons to get a reaction from hundreds, eventually creating person C, whose overreaction, sanctimony, and hypocrisy will provoke reactions from people D to F; who were not trolls, but can't help trolling person C. Their reactions are followed by the outraged reactions of people from G to N, and so on, generating a massive amount of energy. It's like a fission reaction followed by a fusion explosion, all bringing out the worst in humanity." Impeccable!
In other words, what the Axiom of Trevor states, according to South Park, is simple: trolls don't seek to insult a person per se, because that would be too little; they seek to strategically sow the seed of discord, ultimately achieving an unmanageable ball – with a mind of its own – of crap, hatred, and snot. That seed doesn't necessarily have to come as an insult or offense, but it's designed to generate the overly sanctimonious and hypocritical reaction from one or more users, thereby calling other people (who are usually not trolls) to troll those users for their overreaction; and so on.
In this way, with minimal effort, the troll exponentially multiplies their efforts, infesting minds like a virus, outsourcing their war, and making us all end up angry with the rest of the world, sowing hopelessness, contempt, and resignation among mortals.
But don't worry, the vaccine is already applied: now that you know how trolls operate, you're (almost) immune to their evil plans. Use this knowledge wisely and remember that the best way to fight the monster is still not to feed it, as the old and always valid web adage says. Besides, friend, think of it this way: no problem worth solving will be solved by insulting or correcting anonymous people on the Internet, participating in toxic debates.
By being part of the troll's game (from either extreme), you'll only become another link in that chain of hatred with which we keep ourselves captive, thus allowing the true villains (like Mr. Garrison, in this case) to get away with it. Don't be an accomplice to misanthropy!