It's not that I'm offended by insults. I quite understand I'm a far better person than the other. I'm annoyed by insults. I'm annoyed that I'm trying to play while someone is harping on every minor mistake.
Let's go with the yapping dog scenario.
There are 5 players in a room. One of them is a tiny yappy dog. The shrill annoying kind. Four players on the team are trying to concentrate. The fifth is a yappy dog. He's playing, but he's also yapping. I do something wrong. Maybe I give up first blood. It happens, nobody is perfect, and the dog comes over to me and starts yapping right at me as I'm trying to concentrate on playing.
If they eventually go away, I won't report them. But if that dog keeps yapping and yapping and yapping, attacking my ears like the sting of bees at every moment while I'm trying to make up for the mistake I made, it detracts from my play. In fact, I've had a jungle so on my case I ended up giving up two towers trying to wrest blue from him because he wouldn't give me blue or come into my lane because of a single missed gank. At a certain point, the yapping gets so distracting I can't play.
So I ask the management to come over and remove the yapping dog. League of Legends is a game after all, I'd like to play it and enjoy it and relax without yapping dogs. Most players don't want a yapping dog.