For me, it's more a matter of repetition. I like games with progression, and progression in multiplayer games essentially requires repetition until you get better than everyone else, which I get tired of fairly quickly.
There's that, which is why there are very few multiplayer games I play for long. I did enjoy Wipeout 2048 on the PS Vita, which basically had a multiplayer campaign where you would be set certain tasks. The early levels would require you to simply complete the race - didn't matter if you came last - and it moved up through to objectives like hit another player with a weapon, destroy another player, don't come last, be in the top half of the leaderboard and so on. It works astonishingly well, and achieving an objective even when the other seven racers have handed your ass to you on a plate is still very satisfying.
But in any case, I do get the feeling that I'm surrounded by assholes when I play online.
I got Wipeout HD Fury for free when the PSN temporarily exploded, that is a really fun game. I prefer playing multiplayer in split-screen with friends, since then you can actually talk and stuff, it's kind of a different experience. Though playing Wipeout HD on a big screen (we have a projector, so our screen's pretty large) may cause vertigo and seizures for the weak of constitution. XD
And yeah, the asshole problem is why I frequently stop playing League of Legends. I enjoy the game, but I hate playing against other people, so I usually just play bots which gets boring after a while and then I stop playing.