Facebook has only "Like" button. Would you like the creator of Facebook to also add the "Dislike" button?
I think the reason that Facebook hasn't taken up the opportunity to introduce a "Dislike" button might be to keep the atmosphere on people's walls positive. Introducing a Dislike button might make people argue and then Facebook could be blamed for being a platform for negative socialising... But I'd think it'd be fun to see a few people get annoyed that someone doesn't like that they've "just woken up and made some cheese on toast".
I don't understand how it would work. What happens if you click "Dislike" on a fan page? Do you still "become a fan"?