Part of the reason I intensely dislike people who put their own fun or sense of self-righteousness before other people's emotions is that emotions are an aspect of the psyche. A lot of what these people do is harmful to other people's emotions, and thus harmful to their psyche. In short, their asshattery is causing quantifiable harm to other people.
That's not to say that this is permanent harm. Like most physical cuts and bruises, emotional wounds can heal. In fact, sometimes they can heal even quicker than physical wounds. However, just like real gashes and broken limbs, deep enough wounds can heal wrong, leave scars, or become "infected". In short, people don't realize it, but their mockery of other people is actually harmful on some level.
At best, an emotional wound can heal in seconds. At worst, it lasts for a lifetime... and can end one very quickly.
As far as developing a thick skin goes, yes, that much is true. However, this is also victim blaming. While developing a thick skin is always wise, it's not something you can do on command, and it shouldn't be the victim's responsibility. It should be the jerk's responsibility to not be a jerk. Not to mention some people, especially those who suffer from depression, are sometimes unable to develop that thick skin.
The correct social response to acts of bullying and causing emotional harm to other people is to discourage it. Unfortunately, because of various social effects, what ends up happening is that the asshole is lauded for being an asshole. All sorts of justifications and victim-blaming are use. It's even mocked. "Awww, did your fee fees get hurt? lol."
Yeah, emotional harm isn't exactly the end of the world, but it's not as insignificant as being nothing. And what's worse, people think that because it's said over the internet, it should be treated less seriously. If it would be abuse to say it in real life to another person, it should be considered abuse to say it on a forum or in a chat room. But because people perceive it to be less serious, they're more likely to be abusive.