Soldiers look more professional without facial hair. That and everything pointed out by Platapus and August (EDIT: and Aramike), especially uniformity. The idea is to get multiple individuals functioning together as a whole, and stripping the hair away helps that indoctrination along. So if the man wants to serve he'll just have to suck it up like everyone else and shave. If he won't do that then he might not be a good fit for the military. It's only temporary; he can grow it back after he's done serving.
