Good thing you are an expert lol
The major wanted me to stay and the squadron commander wanted me to stay (in fact he refused to let me leave for a while). They only let me out because I asked to leave (with the excuse of my medical condition) which was waived upon entry. He gave me his recommendation so I could get back in the military with no issues if I actually did decide to come back. I wasn't kicked out. I don't know what branch you are familiar with, but the Air Force doesn't exactly just kick out airborne linguists. For the most part everyone getting separated had to fight to get separated. I knew people who had been on med-hold for over 9 months. I'd rather spend that time more comfortably in the civilian world where I actually have a bit of freedom.
Depending on why people get separated, the Air Force won't want to waste their time with certain individuals. For example, if you just want to go home and are completely fine, they would never let you back into the Air Force because you wasted their time. If you leave for severe medical reasons, you probably won't be allowed back in either. The only way to get a recommendation to rejoin is if you have a legit reason to leave, and are actually worth letting back in.
Thanks for your omniscience on the situation though, Ragnar the Red.
I was in the Marine Corps, and I didn't claim to be an expert. Every single medical condition that warrants you to leave the military, warrants you not to be able to return to service. If you choose to leave, based on this specific medical condition, and you think its that serious to not finish out your contract, just because some Major says he recommends you doesn't mean anything. Being let back in will be a lot higher decision then just a recommendation, they'll look at your decision, and medical condition and say "Hey he thought it was serious enough to leave", 99% of the time (especially in the shrinking military now) they won't let you rejoin because you left saying it was serious enough to leave. Maybe the Air Force has a different policy then the Navy or USMC, but I doubt it.
"For example, if you just want to go home and are completely fine, they would never let you back into the Air Force because you wasted their time.", the only time this will ever happen is during BMT training no where else. If you want to just "Leave" the military, that won't happen, you will have to do something to warrant a discharge and usually that is negative. No way in hell can you get out of your contract because you feel you're done.
If you left because of a medical condition, you have 0% chance of getting let back in, because they're not going to take another chance on a variable.
p.s. How long did you serve (just curious) ?