I think that they don't simply do it to get a reaction out of who they pick on. They do it because they want to feel superior, and to do that they have to make their target look like they're as low as dirt in comparison to themselves.
When someone reacts to them, it isn't the fact that they're reacting that makes the troll feel like what they're doing is working. It's how the person reacts. People, us furries included, tend to get defensive when someone trolls us about our beliefs. Even if we believe there's nothing wrong with being furry, we know that society thinks there's something wrong with it and therefore we feel we have to defend ourselves when someone trolls us.
Now, when someone gets defensive against a troll, the defendant immediately begins to look like the lower out of the two. If there was nothing wrong with being furry, the defendant would have no reason to defend themselves.
Another problem is that the people who do take an offensive stance often do it weakly. It's usually "well you're doing something wrong too", which is still defensive. "Well, you're ruining the earth." for example. Not only do they get to pick on you for being a furry, they get to pick on you for siding with the scaredy-cat environmentalists as well. Not that I think there's anything wrong with being environmentalist. It's just that environmentalists often fight back weakly and defensively just like many furries do. Either way, wording your retort like that puts you in a defensive position.
And even if you do take a strong offensive position on them, perhaps hurling insults at them, the most you're going to get on them is equality. You won't be a subordinate to pick on anymore. You'll be a challenge that they won't be able to step down from if their pride has anything to say about it. You're probably still going to look lower than them because you're reacting to them, which means that you must be lower than them if they can bother you.
The trick to this is to become their superior. You have to speak to them in such a way that you make them feel like they're the lower one. You have to speak to them as if you seriously don't care about them. Speak calmly. Don't lose your cool. Speak your insults to them indirectly, in an implied manner so they come to the conclusion that they're being insulted rather than you making it clear to them. You don't have to directly insult them because if you're better than them, they can't bother you, and therefore they don't merit the attention for an insult.
If you become the one who doesn't care about them and they continue to insult you, it's because they've been placed in the position where they're having to start looking up at you when they talk to you. They don't like that, and it bothers the hell out of them that they can't bring you down to their level. Put them in the defensive position for the win. They might not stop attempting to bring you down, but that way you are the winner and they feel like the loser.
Maybe it's because I'm a nerd (and proud of it). Maybe it's because I'm a Wolf. Maybe it's both. But I've spent a lot of time thinking about things like this from time to time. Considering why people act and react the way they do and putting it in the perspective of dominance and submissiveness. I think that in order to win against these kinds of people, you can't look up at them and defend yourself from their onslaught. You have to be able to at least pretend to look down your nose at them so that they are the ones who feel bad instead of you.
EDIT: Coming to that conclusion is one thing. Practicing it is something entirely different. Haha.
I can force myself to do it that way online if I need to. But I'm too shy and easily intimidated IRL to ever stand up to a troll in person like that.
ANOTHER EDIT:
A good example.
Troll: You ***********
You: Whatever, loser.
It's a bit direct, but it's still nice in that you're not only dismissing them as a loser, but you're dismissing them! You're not even putting forth the effort to explain to them why they're a loser. You're just shooing them away. Shooing them away not only implies that they're not important enough to maintain your attention, but it makes them seethe with self-doubt that you think yourself far enough above them to be able to dismiss them so easily.
LAST EDIT, I SWEAR:
When you really think about it, the troll is already lower than yourself for going out of their way to try to insult you in the first place. As long as you don't let them get the upper hand, the win is yours.
Partial censorship is not allowed.
Ephemral