You picked a game that is infamous for its toxic and impolite community. Amongst other genres, the MOBA genre itself has a problem with unfriendly communities, it's not just an issue which occurs to League of Legends.
MOBA games usually are free to play so they attract many players, especially the ones who can't afford an AAA title, e.g. younger players. League of Legends also has the advantage that you can pick it up more easily. This allows a lot of more casual players to play the game since they have the same gaming experience as other players who invest more time into the game. This, together, results in the massive stats which are produced by the game. A short summary:
It's a widely known and played game which has a lot of young and casual players.
This is the first reason why the community is so toxic: Younger players just haven't learned how to control their emotions yet so they accidentally disturb the experience during playing. Whilst most young players don't do it on purpose, there indeed are player who do it on purpose as mentioned by @MichaelFrank. It's a cool and common thing to do - it shows some kind of braveness to do it, also it's a way to show off your creative ways of offending and insulting. (You may not believe it, but some youngsters are competing about the "best" insult.)
Another reason is the multi culture aspect in the game. This thing basically affects every multiplayer and co-op game. You are thrown into a game with people of different nationalities. Communication differs from nation to nation so misunderstandings are to be expected. Although player A just meant to be funny by saying "You little ass :D", it's misunderstood by player B, who received it differently.
And if the multi culture aspect matters, so does the age difference between players, too. Older players usually are more polite towards the community, while younger players like to say things straight. This can lead to some serious problems because older players might see their straight way of communication as an offend. Would you rather receive feedback more politely or more directly?
The polite way:
Oh, that way messed up over there. Can you do things like that the next time, please? It would really help to win this game.
The direct way:
You fucked up there.
This can result in problems since not everyone wants to receive direct feedback.
The culture and the age difference of gamers matter since they affect the way of communication and the play style.
The casual players are a "problem", too. What do casual players do? They play. Why? Because they want to have fun as fast as possible. They don't want to hear your elaborated strategy, they don't want to play a support who sacrifices his gold for the sake of the team, they want to go on a rampage by killing as many player as possible. Of course they are happy if everything works out just fine but if not, beware, it's all your fault! Admitting faults is way harder than blaming others.
Casual players want to have fun as soon as possible. If something goes wrong, it hurts their goal of happiness.
One more serious problem is racism. I bet every gamer came across a situation where was said:
All (add nationality) players are bad because the player I met the match before was bad.
Well, often people with Russian names are insulted when the game starts because there are a lot of Russian players, hence there are a lot of not so good players too. Also, there are players who are a little bit unforgiving for historic actions done in the past, e.g. Segregation, Holocaust. They will always will call you a (add any kind of insult) for something not being relevant to the (most) games.
Racism is a problem in the gaming world as it's in the real.
I'm really sure that there are other reasons too but I wanted to share some possible solutions for the reasons I mentioned.
As always: Don't feed the troll. It seems so basic but it truly is a time and nerve saver. However, this is how users may handle it since they lack moderator power to punish people - ignoring most likely leads to a lack of interest of the troll.
If you come across a possible game disturber, mediate between concerned users, rules and the user itself. Show him that there are rules for the game and that users might get upset if you're not following them. Add a report function which works as following:
- Everyone has access to it.
- Everyone is allowed to report.
- Reports for exact rules violations.
- User gets punished if reported several times.
A punishment mustn't occur if the player got reported just once. A report may happen out of hatred and emotional things so it's important to protect users.
Set up preferences for users so they join games which are hosted on servers in their country where they can meet users of their country. If you can destroy the confusion about communication between users of different nationalities, you will receive less reports. Nevertheless, it's somewhat difficult because you don't want to limit them to predefined servers, you just recommend them to do so. If they feel like playing on another server, you mustn't take actions against this desire, it's their good right to join whatever server they like to. Still, you can remind them that they are playing with other people of another country so they should (must) speak a language which is widely known in this community. If they hinder their team by speaking in an inappropriate way, you should make an example and ban the particular user to his "home" server.
Search for other gamers that share the same point of view as you. You aren't able to play peacefully if you play, as a casual, with a professional players. That won't happen due to the different points of view. A casual player wants to have fun, a professional wants to win. Don't go in with more serious players if you aren't really interested in game tactics and strategies, otherwise it'll just harm the team.
@Carl said that the topic is really lengthy. It indeed is. I can't tell you all the reasons with the time I have, but I think I covered the most common things.