Punishments are given out in this order:
1.) 10 game chat restriction
2.) 25 game chat restriction
3.) 14 day ban
4.) Permanent ban
The way it works is once you receive one punishment, your next offense will give you the next highest punishment, regardless of how "minor" the offense may be. Now, it is possible to be escalated straight to a 14 day or permanent ban without any prior punishments, but Riot really only does this if they deem your case severe enough.
Knowing this, unless you were exhibiting very extreme toxic behavior in that one game, you WERE NOT permanently banned for just that one game. You were permanently banned because you received the other 3 punishments, which serve as warnings that your behavior is unacceptable, but you continued on with the behavior that got you those punishments. You essentially showed Riot that you have no intention of improving your behavior, so they decided that they no longer want you in their game anymore and permanently banned your account.
If you truly believe that this punishment is unwarranted, you can choose to post your chat logs to see what the community thinks about them. We could help give some clarity as to what lead to your punishment.
Also, something to keep in mind, the whole "he was doing it first" argument does not work. It doesn't matter what other players are doing, if you choose to retaliate back with your own toxic behavior, you will be punished.