This subsequent assertion calls into question the validity of his statement in the first panel, and the reader is to assume that Garfield doesn't really have a right to sing the blues, according to anyone else but himself, but doesn't care if anyone else thinks so. He demonstrates this in the last panel, by asserting that he has the right to something that he certainly does NOT have the right to, according to anyone else's opinion but his own.
The joke involves the fact that Garfield has a selfish and self-important personality, and doesn't give much regard to anyone's opinions but his own.
