I imagine at least some part of it has to do with the natural human resistance to significant change, especially when it doesn’t involve you personally. If you’re not a gay military member, then it’s harder to see why things should change, since things seem to be functioning OK.
Personally, my view is that the onus should be on the people proposing the change in the policy to show how letting in open homosexuals will make the military more effective (or, at the very least, show how the change will be neutral in this regard). If they can do so, then I don’t think there is any valid reason to disallow open gays from the military.
As it currently stands, homosexuals can serve in the military so long as they maintain discretion. From what I’ve heard from friends in the military, unless a gay soldier goes out of their way to show their commander they are gay, most commanders will ignore this rule if following it means kicking out a good soldier.