I saw a pick where it said "What else should Fanpop have?" created by breebree446. There was the option of "Unsubscribe Button". Actually this button exists, just have to follow some steps.
1. Go to your own profile and go down to the "My Clubs" part.
2. Then click on the "more clubs >>" button.
3. Below each club there's an "unsuscribe" button.
4. Click on that button and
Now you have the oportunity to unsuscribe a club, is really easy and like this you won't be a fan any more from any club!