This is actually two separate questions:
{quoted}
Please explain, please explain to me how they had to put up with me, [...] I don't know how that's my fault, [...] so that's my fault?
You are responsible for what you say. Not anybody else. No matter how anybody else is acting, you have the choice of how you react.
Your behavior is your fault. If you choose to react in a way that the League community does not consider acceptable, you need to figure out how to change that if you want to stay a part of this community.
I would advise you to react in the way that Riot Tantram suggested:
[{quoted}](name=Riot Tantram,realm=NA,application-id=ZGEFLEUQ,discussion-id=dBcmRkNo,comment-id=0002,timestamp=2016-07-22T17:41:28.314+0000)
The next time you encounter that player spewing off hate speech, just mute them and report them after. There is no reason to ask other players to report them.
If your teammates are acting in a way that you don't consider acceptable (after all, you're part of the community, too!), you can express that by reporting them, and they'll be held accountable for their behavior just the same as you.
{quoted}
why not give them chat restrictions too for what they did, the Nidalee and the Thresh both sitting there flaming the whole entire game [...] she did nothing but feed the fire
If you reported them, maybe they did get chat restrictions. Quoting Tantram again,
[{quoted}](name=Riot Tantram,realm=NA,application-id=ZGEFLEUQ,discussion-id=dBcmRkNo,comment-id=0002,timestamp=2016-07-22T17:41:28.314+0000)
Getting reports beyond 1 does not increase the chance or speed of a game being reviewed.