Many people are totally unaware that they can't sing, and cannot be pursuaded of the fact. You only have to watch the X-Factor auditions to see this.

Mrs Pavane, in her career as a club singer, has encountered a few aspiring performers who have about zero chance, in one case a girl being supported by a father who was equally unaware of his daughter's shortcomings as a singer, and couldn't understand why we could not recommend her to agents.