PROTIP: The constitution does not apply to the armed forces.

There is no habeas corpus. There is no 1st Amendment. There are none of the niceties we take for granted. So when the AEC tells you it's perfectly safe to charge into a nuclear blast, even when you prove in a court of law they were lying to you they get to say "too bad, so sad, shouldn't have joined the Army."

Affirmative action has nothing to do with it - Affirmative Action is all about recognizing that some people face more hardship than others (theoretically). Al Franken's analogy is the best I've found for the theoretical basis for AA:

Consider two baseball players who tie in a race to first base. However, one runs with perfect form while the other runs awkwardly. Which do you choose? You choose the one who runs awkwardly because when you teach him good form, he’ll run faster than the other player. Black Americans are nothing but awkwardly running baseball players, so affirmative action is justified.

"Women in the military" isn't about "women need a leg up in order to compete with men for military jobs" It's about "women need to not be dismissed by edict." To use the baseball analogy, it's allowing both people to run even though one of them is a girl.