League of Legends has become one of the biggest games in the world, but it is equally well-known for its vitriolic community. Not everyone that plays League is a jerk, of course, but if you play, chances are you're going to experience it sooner or later. It's largely unavoidable.
It's a video game, on the internet, so really there's no surprise that there is some trash talk and name calling taking place. But why there is enough of it that the players have earned such a unique reputation above and beyond most other gaming communities, I think, is attributed to a couple of factors.
First is the sheer number of people playing the game. The more apples you throw in the barrel, the higher percentage of rotten ones you'll have. But also I think it has to do with the type of game that League is... a top-down action battle game. You can very clearly see what everyone else on your team is doing (or not doing) at all times. Far more so than if you're playing a first-person shooter.
In a shooter, dying may elicit a "noob" or slight trash talk from an enemy or teammate. In League of Legends there are so many other levels on which to be criticized. Your item build, your positioning, your last hitting, your jungle route, whether you gank enough or not, which enemy champion you focus, even which champion you pick to play. And everyone in the game has their own idea of the "right" way to do all of it. With so many different little things for people to rage about, it may all rise above a murmur of hatred, to a deafening din of toxicity.
It's gotten to the point where Riot has now put together a special team on staff, including a number of PhDs in neuroscience and behavioral psychology, to help find ways within the game to both curb negative behavior, and promote positive behavior. I wish them the best of luck, because every time I play solo queue, all I can think is "those poor bastards..."