Trump was not a draft dodger, was ruled unable to serve due to bone spurs. That's an actual thing as opposed to getting your doctor to say you have asthma.
And, btw, I've served alongside several people who had asthma, they didn't use that as an excuse to turn their backs away from the call to protect their country. I've seen many people lose their careers over bone spurs, too. Bone spurs are no joke (and are empirically proven in x-rays) and I can't imagine what hell they must going be going through while running 3 miles with an 80-pound ruck.
Edward Snowden lost his ability to serve as a result of the same hairline fractures that can cause bone spurs. Why would anyone want someone to waste taxpayers' money or go through that kind of inhumane torment for no real purpose? Serve may a year and break a leg? It doesn't make sense.
Asthma, however, easy to fake. Even if your dad is trying to force you to join the military, you can lie and tell them that you have exercise-induced asthma. I've personally seen a rich kid do that to get out of the military under those very circumstances. His dad demanded that he does at least one enlistment. He was talking about his plan on the ride over to the meps to get out. Sure enough, he was the only one of us that came back from the meps without entering into service.