aggiechad, asthma is not something you want in somebody who needs to operate in a high stress, physically demanding environment where you can die in a few seconds(like infantry, aviation, etc.). Especially like in some aviation platforms where if he has an asthma attack there's nobody to back him up.
And asthma is NOT the only condition that automatically disqualifies you from the military. Others include being blind in both eyes, having developed a habit of compulsive lying, being actively gay, missing both legs or arms, not having a brain, among others.
OK but seriously there are other fairly common things like heart murmurs(I hear this is something waiverable if very minor and depending on type of murmur), eyesight obviously(also waiverable under right circumstances), hearing(again with the possibliity of a waiver), not being too freaking tall, etc.