As zPOOPz mentioned, zero-tolerance chat behavior (hate speech, encouragements of self-harm, death threats, etc.) can warrant skipping the first two punishment tiers; all three punishment tiers, even, in the case of death threats.
You're only presented with your chat logs because the punishment is dealt based on your behavior, nobody else's, and that you're supposed to be looking at what about your behavior you should be changing going forward. It doesn't matter if anyone else in the match was also being vulgar or breaking the rules; you participated, and you need to learn not to.
You can consider that unfair, but the fact of the matter is that adding other player's chats on top of yours would be pointless and detrimental to reform.
And, if you're going to try to discuss behavior, you're gonna have to give more explanation than just "not spelling out the hateful words". Just speak plainly; so long as you're not naming and shaming, you can't really do much wrong in holding the discussion.