So I have a very thin skin, and when I argue with someone after a game I let it get to me emotionally. All too often they just leave before I can say what I want to, and I'm left feeling like I have unfinished business. This feeling can sometimes persist for days. How can I not be so passionate about arguments in League?
You mute them as soon as they start being toxic. While they might cause some distress with their first toxic comment, you'll have forgotten in a minute or so as long as you prevent any further chat from them.
Don't stick around in the post-game lobby to let them continue, either.
Seek medical help.
Stop caring about what random people on the Internet say
you care too much about what you think others think of you.
truth is, they only care about themselves. (And most people just want to go play the next game in peace without the same person argueing with them)
It's tough to judge w/o knowing age, but in general its best to develop a thicker skin.
You're going to be insulted, many times, both to your face and behind it. If you let it control you then you are going to have way worse issues than your League experience.
It might help to try and put yourself into their perspective, their mindset. It can usually be easy to see why someone is behaving the way that they are. This might also help to not take things so personally. These people don't know you, they are just reacting to something from either you, or the game. What they say doesn't actually mean anything.
Finally, don't argue. It's a huge waste of time and effort and is just going to drain you emotionally and get in your way of enjoying the game and being a good teammate, which is the whole point of the game. Whether you are playing with trolls or pros, in general, you will get the most enjoyment out of focusing your energy on being a good team player, whatever that entails, and ignoring the provocative actions/words of the other players (Or simply quitting and taking the queue penalty).