I got a 14 days ban for calling a teammate ''%%%%%%'' 2 times, and that's all. I know it was a bad thing to say and all...
It's not just a "bad thing to say", it's hate speech. And judging by the letter count, it's either a homophobic or racial slur. You should know full well exactly why you shouldn't be saying it.
Two times is two times too many. You'd deserve a ban even if you said it once. You're not allowed to use hate speech, full stop.
I was not trying to pick a fight, in fact just loosen my teammates up because they were really hot headed...
If you want to get your teammates to loosen up...Calling them racial/homophobic slurs is probably the absolute worst way to go about it.
Crack jokes, divert their anger to something constructive, reassure and assuage them - that's how you get people to loosen up. What you did wasn't even in the barrel, much less scraping the bottom of it.
if yes, please tell me what else have I done wrong, I'm willing to learn from my mistakes.
I'm afraid I can't see your screenshots; I may just need to jump in/out of the post to see them, or it could be an issue with the formatting, but once I do see them, I'd be glad to give a peer review.
EDIT: Yeah, just had to come back to the post. Dunno why that happens.
As for your logs, on top of the homophobic slur, you spent an unnecessary amount of time arguing with your teammates, harassing and agitating them, as well as excessive complaining about the enemy Aatrox.
If teammates start getting hot-headed and start arguing, your best bet would be to mute them, not to meet their rise and argue with them. And, for real, I don't see how anyone is going to loosen up when being called a homophobic slur. Nobody is going to respond well to flame and insults, especially egregious ones like those.
And, yes - excessive complaining is punishable, though moderately so. It detracts from the game, and drains team morale to have that one guy obsessively complaining about their lot or some aspect of the game.
Were it not for the hate speech, this chat log likely would've simply earned a chat restriction.