This is type of deferment is pretty standard. My son has asthma and played high school sports (cross country and soccer), but he would still not be allowed to enlist in any of the services. As far as I know, they do not give waivers into the Armed Forces if you have had asthma, because the risk is too high.
Understand but Biden was also a lifeguard. Swimming requires lung capacity and breath endurance. In the military or in the swimming pool having an asthmatic condition could put people at risk.
Even with a “supposed” asthmatic condition Biden has been a blow hard all his life.