My sufferer also has a lot of contempt for what he considers, I guess, the herd or mob mentality (his favorite is lemmings, rather than sheeple, though. :chicken:). It comes out infinitely worse when he's symptomatic. He's also not in treatment (and has had minimal treatment in the past), and does not have the tools to deal with anything when he is symptomatic.
When he's not symptomatic? He can curb the arrogance, and realizes that everyone is different, and just because someone doesn't think like him, doesn't have the same life experiences as him, it's ok. He may have knowledge in one area, but someone else has knowledge in another, and that is valid. Politics don't matter, all men are created equal, and equality issues of race, gender, and sexuality are important.
When he's symptomatic? All filters (and it seems, positive opinions) are gone. I'm an idiot lemming for having a college education (and I "look down on" him for not having one...spoiler: I don't actually look down on him, never have, never even suggested it). Anyone who has any beliefs of any major political party is a lemming (And shill. And libtard, if liberal...ironically, conservative folks are still ok). Racism is dead, and anyone who claims otherwise is keeping it alive (and is a lemming). Anyone who makes a big deal out of gender is a lemming. Anyone not him has no idea what it's like to suffer (and he'll even rail about other people with PTSD "faking" or something...I usually stop paying attention to the rants).
Is he an arrogant asshole all the time? Nope, only when he's symptomatic. Can he control it when he's symptomatic? I don't know, I'm not in his head. But from what I've read here, probably not; he can only control what he does when he's not symptomatic. What is the symptom coming out when he's in arrogant asshole mode? Probably negative core beliefs, but, I don't know.
My point is - for every person here who has a handle on their PTSD and "would never" become a raging asshole when symptomatic, there is someone else who does. Considering how often I see "We're not all alike! Never compare us!" I find it ironic that I also see "I would never do that!" so therefor, neither should anyone else.
And this is the crux of it:
The fact that the little bloke is imitating his dad seems pretty normal to me.
Kids imitate the people they look up to. They absorb a LOT more than we realize. He KNOWS PTSD is a spectre in his world, and it is not a good thing. It really does sound like he's a kid, in a troubled family, trying to make his way in a world he doesn't understand yet. Does PTSD touch him and affect his behavior? How could it not? My advice? Get the whole family into therapy, together.