A direct excerpt from a book:
'They can laugh at jokes; they read every book by P.G. Wodehouse and love his quiet humour; they can enjoy a joke against you. What they cannot abide is a joke against themselves.'
I'd like to know if there is a specific word(noun, adjective) for such people. I don't know how else to further explain my question. Pretty much everything is stated in the excerpt.
Post Answer EDIT: I'm not looking for words related to sensitive-brittle natured or synonyms.
Such people enjoy joke on others but not on themselves. Maybe I'm being too specific, but such people are not at all sensitive, thin skinned or else they wouldn't be making jokes on others.