Just had an incredible argument (long-ish story)

tl;dr: Person did bad-ish thing. Argued with person about it. Feedback?

This is sort of a long story, but I wanted to share it (mostly to get it off my chest) and I hope to receive some feedback. Thank you for your time!

I just lost a solo queue game. I played support Zilean with a Jinx as my ADC. During the game, our lane was camped by the opposing mid laner and and jungler, and before 10 minutes there were multiple 3-4 man ganks on us. We were crushed in lane and the whole game snowballed out of control quickly.

After the fourth or fifth gank, our Jinx said in chat "gg, ff at 20." Three of us disagreed with her, saying that we should keep battling and we could win. Jinx responded that she would keep playing, but she wanted to surrender when we were able to. However, her actions determined this was a lie.

Upon reaching bot lane turret, Jinx stopped to type another message. She wanted to argue with the top laner about whether to surrender or not. I warded river and waited behind my minions for Jinx to catch up. She was still under turret, typing, so I began to take the farm. The lane was frozen about 2/3 of the way up (we were blue side). The opposing Caitlyn and Thresh kept the wave frozen and I kept farming, eventually telling Jinx to stop typing and focus on the game because she was losing CS. She didn't, and then we were dove by four enemies and died again.

Now, fast forward another 15 minutes. We surrendered after losing a teamfight. I had muted Jinx, so I was unaware what she was saying, but other members of the team continued to tell her to shut up while she was wasting time, over and over again, sitting under turrets while farm was going to waste or teamfights were being lost 3v2 when her presence would have turned the tide. So we enter post-game chat.

The other team congratulates themselves, and Jinx declares that she plans to honor the opposing Thresh. The opposing mid laner jokingly asks why she isn't receiving honor, to which Jinx replies "you suck, and Cait you sucked too". At this point I decide to chime in, although I didn't plan to at first, pointing out "Jinx acted poorly most of the game and more or less gave up. She wasted time arguing. I'm going to report her for negative attitude." I added that if they felt like it, I would appreciate the other players also reporting Jinx. At this point everyone in the lobby excluding Jinx and I left.

As I expected, Jinx defends herself. She claims that all she did was ask us to surrender, which was true, but only part of the truth. When I point out that Jinx sat under turret for several minutes and chose to do nothing but argue with her teammates, she denies it. She claims "I never sat under turret like that." When I state again that she did, her response is "yeah but everyone else on the team told me to." Now, the team all agreed that everyone should "play safe." Those were the words used, no one mentioned hugging turrets except for her. When she was underneath turret, typing, the wave was frozen in the lane, the river was warded, and the opposing laners were in their lanes.

At this point, Jinx suggests I am blaming her for the loss and that I need to self-reflect rather than blaming her. She also insinuates that I am behaving like a child. I accept responsibility for some poor play, but point out that unlike her, I did my best to contribute fully for the whole game. She responds that she did the same, however, she doesn't believe I did.

She then switches topics, claiming that I "assumed she was mad" and that I "let my emotions get in the way." I dismiss these claims, as they are neither true nor relevant to anyone's behavior. I suggest that she ought to understand what she did that earned her the report, and that she ought to understand why her actions were wrong and detrimental to the team.

She denies this, then immediately switches subjects again, claiming that I am upset with her because she types slowly. My counter to that is "it doesn't matter how fast you type, it's about choosing to type rather than play the game." This is where the argument "ends," as she says she is "counter-reporting" me and she calls me a troll and claims I am toxic. I ask her to reflect on her behavior and please attempt to improve, she leaves the lobby, and it is finished.

Now, I was left slightly befuddled. I don't understand why this person wouldn't accept they were behaving poorly, and I don't understand what they perceive I did that merits a report. However, It's all said and done at this point, and I will move on to my next solo queue game, where hopefully the company is a little bit better.

I just wanted to share this story, and gain some feedback about both of the behaviors involved in the scenario. Does anyone have any tips for dealing with this type of person? Is there a way to politely make them see their mistakes and/or help them change? Thank you for reading. Good luck in solo queue.