which one?

So I just had a hilarious game and I want to know what you all think. Props if you read it all.

Last game, I was kennen with 20 kills and kayn had 23. The first time when i rotated mid around 20 mins that game and I took 2 mid towers and mid inhib, the kayn was just running around the jungle farming jungle camps despite being fed right? So we don't take any objectives after we take mid inhib despite having super minions now and 2 people on enemy team is defending mid, but its all good i was just chillen. Then mid inhib was up again and so I decide to go and take mid inhib a second time right? Meanwhile, kayn is still running around the jungle farming and trying to get kills by picking people off. So in my head, I realize that if I keep trying to push lanes whether it was mid, top, or bot, the kayn is not gonna group. I was sitting with 2k gold and full build and so i decided to just sit at mid and defend, no longer engaging with kennens ult or trying to fight 4v5. I mean sure we were winning a lot of teamfights, but the enemy was slowly getting strong with time while kayn was never with us. Only time he was around was to kill steal basically and clean up after we are all dead. Eventually, Kayn gets caught and dies and this enables the enemy to take baron. They start pushing down our second mid turret, me and 2 other teammates are defending while kayn respawns and walks up to us. He was just a flash away from us and then randomly decides to go through the wall and roam up towards baron and enemy red buff despite our mid being taken down. Enemy takes mid second turret and backs off because 2 allies got low. Kayn is still in enemy north side jungle trying to get a pick off but this time gets ambushed by 3 opponents and desperately tries to flee but ultimately dies. He pings for us to go secure elder while he is dead but I am just chillen defending mid rather than going to 4v5 an enemy with baron buff. They get elder and kayn pings missing over my head. Then the enemy pushes down mid taking our inhib and nexus. Kayn says i threw the game because i just sat in the back doing nothing. Lol, i mean, to me he already showed he cared not about working as a team in a team game as he would just run along in the jungle all he wanted without a care about his turrets so now that he died and we lost the game he gets mad at me? Who is at fault here?