Well, what it means comes on several levels...
It can mean any or a combination of the following things, and perhaps a couple others in some situations.
1) Won't take orders. Seriously, some people just can't do this. They were class clowns, slackers, skipped school, never obeyed their parents, you get the idea. They just won't take orders. I'm afraid I do have to judge the lot: they're usually twits. Sorry if this applies. That said, consider how awful it would be in the army, etc. Dude challenges every order, Why me? why not Jimmie-Joe over there?, Why always me?, Looks dangerous Sarge, I think I'd rather see Billy die than me, Say Sarge, is there any way I can destroy unit cohesion and morale today? You get the idea. I'm not talking refusing unlawful orders like shooting into a house you just saw a child pulled into. I'm talking about the boobs who just won't take orders. As a parent, you should know right off if he's this sort. Take the blinders off though, as a favor to him, because this is the Number One reason for this discharge statement.
2) He lied about something like color blindness and, with or without the help of his recruiter, got through the tests designed to catch that. This not only means he fails to qualify for many jobs the Air Force has. Just about anything working with electronics, bombs, and so on. Load it out with the bombs with the green cross on the tip. Hey moron, does that look like a green cross??? That's a red cross, you could've made the mission worthless, the pilot's life risked for nothing! Sad to say, this almost always involves the recruiters telling recruits how to cheat the tests. But eventually, it catches up with the recruit. He is usually discharged, sometimes after being offered jobs he typically didn't/won't want, but for the convenience of the service, not for failure to adapt. However, if someone had a hard-on for the recruiter and he refused to help take him down, the price could have been giving him this less palatable official reason. It would be true, though, since the military, Air Force definitely included, is all about accountability and personal honesty and honor. Being a part of the deception is bad enough, but mentioning the recruiter was part of it, likely the motivator, then clamming up and refusing to further incriminate him (gosh, no one likes a narc now do they, so let's let the harm continue), well, that's not consistent with personal honesty and honor and definitely not with accountability. If I were handling his case and this is the worst I could do, I'd do it. And I'd never just let him off the hook with a convenience of the service reason for the discharge.
3) Being certain he used or sold drugs during boot camp but being unable to prove it. This is simple to understand so I won't belabor it. If you can't convict, or at least get a positive test, but the certainty is there, he's gone. Can't very well tag him with "drug dealer" if one can't prove it, but one CAN make his discharge include failure to adapt. Failure to adapt is the military's way of answering future job interviewers who want to know if his previous employer would re-hire him. It's basically a "H-ll no!" (We do the same in the company I work for: answer no questions at all about the past employee's performance, or give him a glowing report, then answer the would you re-hire him with a Not on God's green earth reply. Nothing to sue us about, we either didn't answer or were complimentary, but the point is made with the question that cannot be sued about. Same here. If they couldn't bust him, but were sure, about drug selling usually, but other things too, then they might use this. You're the parent, you make the call.
4) He fights. Not the enemy. His own side. Bad temper, frequent feelings of "being disrespected". Drinks and is a nasty drunk. (The last is unlikely if this happened during or just after boot camp.) Everyone has to be able to function, LIKE A HUMAN BEING, not a gang member or some surly cretin, in a vast team that relies on unit and force cohesion. There is no room here for prickly pears. No John Wayne in "The Shootist." Everyone has to suck it up and work together. Fighting each other flat-out will not work. Kids coming out of gangs directly and out of schools that gangs and race conflict had a large role in have frequent problems here. Most catch on but some just can't do it. Or won't. They just can't break the cycle. And the others egg them on, work their buttons. It's brutal and personally I never understood why the egger-on's don't get sh-t-canned along with the prickly pears. But it's the pears that fall from the tree, not the branches. This one really is mostly given backgrounds so again, you're the parent, you make the call.
5) Some odds and ends are along the lines of he just can't function without 11 hours of sleep, won't get out of bed until noon, only showers "when he needs to", tries to affect a Goth (or other) lifestyle, is suspected of stealing from his unit-mates (look back to being suspected of drug dealing, it's just less frequent), will not work very hard (slacker, makes others carry the load or suffer for his poor performance), disrespectful of authority or authorities at the wrong time, and especially of the idea of military discipline, and instead of apologizing and looking for punishment, argues, or otherwise fails to understand, the situation. A less common one is failing to bring his physical abilities up to minimum though usually that's one that leads to the disrespect for military discipline. The remedial company in boot camp usually leads to a few harsh and demeaning physical punsishment sessions during which a recruit who is over-minimum would fail. Combine a poor attitude with iffy physical conditioning and a couple of those PT sessions and you could easily have the right combination of events to lead to a failure to adapt because of chronic disrespect for military authority. For instance, if he just said no to a punishment session. That's a balloon burster and they don't work with you too seriously after that. You're pretty done at that point. There are more.
More on the idea of what it means though...
It likely means that he got an honorable discharge since the likeliest cause is he just won't take orders. So he just needs to move on.
If he got a "general discharge, under honorable conditions", he can petition to upgrade it after 6 months and every 6 months thereafter (so even if they draw it out and make him suffer a year or two, he can eventually get it upgraded to honorable).
Finally, on what it means...
It means, almost certainly (I mean certainly. I say almost just to be polite and to acknowledge the grinder sometimes grinds the wrong person. But I mean certainly.) that he is a boob. You want to enable that? Want to keep him on that track? Help him be a 72yo boob someday with a long life filled with "reasons" for why everything in it failed to work out and thereby caused him to not feel so good for having lived? Then by all means, ask HIM what happened and BUY INTO whatever excuses (I mean "reasons" of course) he gives. Rail against the service. Support him, unconditionally.
If you want to help him take this as the shock that finally screwed his head on straight, then do so. I don't know, you may be long-suffering on this front — if so, stay the course a little longer. But my guess is your little Billy never did anything wrong and the world is out to get him. (Sigh) So change. You want a sea change in him, maybe you have to have one as well. Don't take his cr-p. Don't bother hearing "the story" more than once. It'll change and adapt anyway. Demand he straighten up and be a mensch. Stick to it. Stop being a crutch. Watch his behavior. Critically, not blindly. See if he doesn't seek to shore up his self-image with other crutches. Kick them out from under him. Stay with it. He's a grown man now and the scale of harm he can cause himself and others is grand, not petit. The Air Force seems to have used tough love. Really tough. Hang in.
His having a good life is the reward.
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