A fabricated or highly exaggerated story intended to deceive.
This is a corruption of a "concocted and bully story". Bully is the Danish bullen, or exaggerated. Therefore, it stands to reason that a cock and bull story is a made up, exaggerated story.
A person who thinks he is a pirate one week and the following week he has a gin in him the also think they have cancer and tell every soul he meets that he is dieing from a brain tumor but yet never receives any treatment and goes back to being a land pirate