You have some good advice. If you want to avoid this type of behavior completely, then by all means use the mute button and use it early.
So if I have an extra bad game here is something I like to watch :
Aphromoo's Solo Queue Wisdom
https://www.youtube.com/watch?v=D61zfM63v60
{quoted}
Me: I'm not the only one making mistakes here
Kayle: Yah but you're really bad
Me: I thought you were optimistic?
Kayle: I was until I saw how bad you were
Kayle: Hard to be optimistic when you see pure garbage
Kayle: Man this thresh is really good, how did you lose lane so hard?
Thresh: I literally set up every kill for him, and he didn't do anything.
Me: (After getting the only tower we ever got that game) Well I got a tower, that's more than any of you can do.
Thresh: so bad
Whatever led to the first line of this conversation was not worth a response. When somebody is just complaining and complaining they are just looking for a comment they can latch onto and attack. I can almost guarantee that if somebody besides thresh* responded they would probably be attacked by these two. If someone is just fishing for an argument, don't participate in it. It just takes away from your concentration, makes you play worse, and then makes you feel worse for playing worse. If someone is spam complaining, just mute them. If they are being really nasty about it, report them after the game. That is the course of action provided you in this game.
*I say anyone besides thresh because you were playing ranked. When you are playing ranked and two people are going off on someone chances are they are a duo queue. They will back each other up instead of admitting one of them did poorly 9/10 times. Also, there is no use saying "You are prolly duo." They will say they aren't, even if they are.
Why are people so mean? Why can't people just not be total fuckwads over the internet?
People are mean over the internet, in person, and in LoL for many reasons. One of the most prominent reasons people are mean online / in LoL is because of anonymity. You don't know who they are, they don't know who you are, and you will most likely never meet in these circumstances again. Unless you are challenger or high diamond 1 where the player base is a lot smaller.
As a side note, this is why when you watch Challenger streams and what not, there is generally more laughing (even in all chat) and less flaming. If somebody does flame it is usually the same person and i've even seen people flame one game then apologize on a later day because they realized they were being jerks. This is because these players play with each other all the time. That wall of anonymity has broken down as the names and players are more familiar to each other.
If you are below that ranking though then the chances get much more likely you will not see each other again. So people will just make you the sacrificial lamb for whatever is making them mad. This could be there own bad plays (example that jungle kayle ganking a fed sivir / morgana lane? They are ahead. And nobody is landing CC on those 2. Horrible idea.), maybe they are on a losing streak, maybe they had a bad day at work, they had a test at school they did poorly on, they broke up with their significant other/had a fight, etc... Anything that makes them feel bad, so they turn to league to make themselves feel better. Also, I have found that a lot of players are frustrated due to a lack of understanding about how to alter the situation they are in. With your example, thresh/kayle were on a losing team and did not know what they could do to turn that game around, so instead of admitting they did not know how to win and therefore had room to improve, they just passed the blame onto somebody else who was also not having a good game.
If you have a bad game, just seek out the areas you could improve on (the best way to do this is via a recording of the game), try your best, and then work to fix those mistakes later. Also, bad games happen.
This trick actually helps me a lot now. I honestly pretend when people are raging, flaming, etc... that they have probably just had the worst days of their lives. This dude just woke up from a coma after having his leg amputated type of day. They may have just lost their job / spouse. They are having some kind of bad thing happen and they came to LoL to try and feel good. However, they are handling it badly. Report them after game by all means if they are being out of line. But in game I just take it as someone having a tantrum and either mute them or just ignore them in chat.
Just pretend it is one of your friends having a rough day, they took it out on you, and they realize it later and apologize. Except in this case you never have to hear from that jerk again!! :}
Work on your own play, play with people who help you build up your confidence, and once you have that confidence this stuff won't bother you as much. And remember to keep having fun while playing this game.