Someone else acting up doesn't excuse your own poor behavior. If someone refuses to stop acting up then just mute, report and move on. Also, you weren't punished just for saying one curse word and you know it, you are punished for consistently creating a negative environment for other players. On top of that, you most likely have already received at least 35-games worth of chat restrictions, hence your 2-week ban. From My Account is Suspended:
WHY ARE YOU SO HARSH?
The Instant Feedback System was developed by Riot Games so that players in the League of Legends community can dictate what conduct they consider inappropriate for a positive gameplay environment. Regardless of the circumstances (such as provocation), behaviors such as in-game taunting, harassment, cursing, offensive remarks, intentionally feeding, intentionally not making a contribution to your team, etc., will be reported and likely punished by the Instant Feedback System.
NOTE: When they say cursing they mean cursing at others and not cursing in general.
I get that your mad but lying about why you got banned and trying to make up excuses to try to justify your own poor behavior doesn't work here. Post your entire unedited chat logs here if you're looking to have an actual reasonable discussion.