When people ban my pick, I play unconventional stuff that I find really fun (example: shaco support) I don't do it to troll; I buy vision stuff, poke, try to peel with my boxes / intiate, etc.
I'd like to point out that a lot of the time, it isn't even personally against you. For example, I ban Zoe every game. I have since the day she was released. I don't do this because I think she's OP or annoying or anything. I do it because she doesn't like me and I don't like that >:(. I did nothing to her!
The point I'm trying to make is that it isn't always necessarily someone banning something just to make you upset. There are many reasons why one would want to ban something. Sometimes it just happens to be your champion. That's not to say there aren't people out there who do it just to spite someone, but it's allowed because Riot allows us the freedom to pick or ban whoever we choose.