I wouldn't say he's dense. It's because of the general situation that he's purposely making himself not take any "hints". He's under the impression that he needs to take care of his best friends little sister while he's away and she's just practicing to be a wife while she's there (you can't pretend to be a wife to your family after all). Nobody's gonna make a move on their best friends little sister unless the friend explicitly tells them it's fine, unless the little sister makes it expressly clear that's the case. Has nothing to do with being dense.