Rage is the result of bad game design
What do people rage about?
"Trolling" - the game matches a player who's playing for fun (and picks Zyra jungle because it's fun) with a player who's playing to win (and wants to see a top tier jungler) and does not have any more fun just because someone else picked something unusual. The division between normals and ranked fails because normals are full of people who just want to beat up an opponent that isn't playing seriously ("tryhards") and ranked is promoted by Riot as the only mode that matters and therefore contains people who just mess around.
- = Lack of proper segmentation along lines of player motivation.*
"Noobs" - it is usually better to make the wrong choice as a team than to split up. The game does not offer any indication of who should be leading the team, and everyone naturally believes their choice is better. When things go wrong as a result of everyone making different decisions, it is easy to blame each other.
- = Lack of voice chat prevents discussing tactics on the fly, leading to losses caused by other people not doing what you believe they should have done.*
"He just lets me die" - the game heavily promotes KDA in general and kills in particular as a measure of a player's skill. However, playing to win means making tons of personal sacrifices. Perhaps you have to suicide in order to save the fed carry, perhaps you should just let the guy who can "only adc" go adc, perhaps you have to leash for the jungler and miss your first cs, perhaps you have to donate blue to your mid instead of keeping it. Playing to boost your own KDA, as encouraged by the game, often comes at the cost of winning the match and vice versa.
- = The game promotes the wrong statistics, even though by design winning a match may require taking a hit to said statistics.*
"Feeders" - mistakes made by another player (and 80% of the mistakes are made by someone else) make the game less fun for you because now the enemy team is stronger. And not just actual mistakes, but also tactical decisions that may harm you but benefit someone else or the team as a whole (not ganking a losing lane). You feel at the whims of your team.
- = The game punishes for mistakes someone else made, as well as for decisions someone else made that may harm you as a side effect.*
"Leavers" - this goes without saying and also falls under punishing players for other people's mistakes. Riot is unwilling to compensate in any way for having a leaver on your team because it might increase toxicity and apparently Riot's anti-toxicity systems cannot deal with that.
- = No compensation for teammates who eat a free loss and waste up to 20 minutes of their time.*
The League community does not consist entirely of jerks, trolls and griefers. The game manages to induce rage in perfectly normal human beings by constantly making them fail for reasons outside their control. An experiment involving a rigged copy of Tetris that intentionally always gave you the worst possible block induced rage in its subjects. That's not an issue to get stomped out by bans. Players should be assumed to be competitive, but players are competitive in many other games as well, and in those games it doesn't turn into unmitigated hate for each other. This is a game design flaw.
Tl;dr people don't tell people to kill themselves, rage inducing games make people tell people to kill themselves.