That's what I thought too, until I saw the father interviewed on the news. He is no more an Arab than I'm a Russian or Hungarian. I think it was his parents or grandparents (or further) who came from the old country.
Now, that said, I've seen what I'll term perhaps a pathological "ethnicity" mindset among children of 100% American parents. I knew a guy (decades ago) who was the son of a guy who grew up in Scotland. The guy's father -- aside from his thick brogue -- was an American, no hyphenation.
The kid, however, when he was in his late teens, decided he was going to get into the Scotsman thing, bigtime. Bought a kilt (and the rest of the costume -- and I use that term because that's what it amounted to for him), a bagpipe, went to court to change his name to something less American-sounding, and went around babbling about finians and orange this and that and take no prisoners, fear the pipes, blah blah blah, like he was some footsoldier in a war a thousand years ago.
In reality, he was a spoiled rich kid, no more "Scotish" than my tuxedo cat is Fred Astaire.
I've seen some other examples, including my sister who in her late 40s decided she was going to "embrace her Jewishness" -- which translates into annoying the crap out of anyone who gets within earshot about her concerns about Israel, how everyone at work looks at her funny because she's the token Jew (wrong -- they look at her funny because she's the token nutcase -- but since she's a social worker, it's par for the course), going to "festivals" (i.e., street fairs), etc., etc., etc.
Of course, she remains a pork-eating atheist, but hey, why quibble about details?
Anyway, it looks from the known evidence to date that this idiot kid was doing the same thing, i.e., "embracing his Arab identity".
The frightening thing is that we have to wonder how many others like that can be out there? Burned out kids with normal parents, who -- on the basis of really nothing more than the spelling of their last name -- will "identify" with the terrorists, and carry out freelance acts of terror.
I've heard that genetics leap frog, i.e. you may be more like your grandfather than your father. I'd say this is true for me. You've heard about bald guys having fathers with hair but grandfathers without? I don't know the mechanics of this myself but have heard it many times. It may be worth studying his grandparents's mental health to see if there's a genetic connection.