Originally Posted by Latenter

This is actually exactly it from a clinical point of view. I don't entirely subscribe to Freud's models, but it literally is subconscious rationalization by the ego as a defense mechanism. See the Wikipedia article.

He probably subconsciously knows you're right, but his mind, unable to cope with being wrong, is creating some reason for why he did what he did; in this case buy a hat with the wrong letter. We all do it, but over something dumb like that, he's probably pretty insecure about himself.