"Fat chance" is ironic. :)

'Fat chance' and 'slim chance' are used to mean the same thing. The difference is 'slim chance' is used literally. The speaker means you have little or no chance of success. 'Fat chance' is slang and it's sarcastic. The speaker doesn't mean you have a big chance, he means you have little chance! Also 'fat chance is most often used as a separate sentence to remark on what was just said. 'You think she'll lend you her car? Fat chance!' For example the interjection 'big deal!' is used in a similar way to refer to something that is unimportant or unimpressive (= not big)

Because they do. It lies in the hunourous nature of the English people.