I agree that people who often miss irony are often very direct, literal people.

One of my favorite movies, "Roxanne," has a great scene regarding irony deafness. Steve Martin is walking Daryl Hannah home in the small town where they both live, and it's a little chilly, so he asks if she would like to wear his coat. She replies, "No I think I'd rather just freeze to death" or something like that. He just looks at her blankly and then says, "You're being ironic! Oh, we haven't had irony here in YEARS!" like it was a consumer item. And of course he's being facetious himself. What a funny, witty movie.