You were banned in game (for a second time) and it has been made clear to you that you are not coming back. You were asked nicely to find another server, but you keep beating the dead horse. You are banned, but you keep trying to find a way around it, lawyering when you know what you did was wrong, and returning to the IRC to keep arguing in game. You were given a second chance, and you wasted it.
And, as for the “broken rule“ you were banned for using a mod. When other people help, they do it legitimately. And the rule did not change. You modified your Minecraft with hacks. Nothing changed there. I closed your previous ban appeal, as it was made clear you were not coming back, and we politely asked you to move on.