Okay, so it's established that Cody is only a minuscule more polite than Jessica, and he just stood there giving off hostile vibes to everyone. He didn't show off his own HoH room, or at least if he did, it wasn't shown.You're not required to be there for 'Who wants to see my HoH room' but it's an established show tradition and not being there is a snub and sign of intentional disrespect.
He very likely couldn't care less about the traditions of the show. All he's there to do is pick off everyone else and get the money. He doesn't even seem to understand that part of the purpose of the show is to have a little fun along the way.
Nitpick: Every time I see him or Jessica wear that baseball cap with the frayed brim, I want to reach into the TV with a pair of scissors and snip off the frayed threads. For some reason that really bugs me.