Answer

The claim that there is no halakhic problem with military service does not require explanation. The claim that there is a problem does require explanation. People discuss it from the standpoint of authority over the young woman, but that seems to me irrelevant in today’s reality. They also discuss it from the standpoint that a weapon is a man’s implement, but that too is questionable. Today that is no longer the case. In short, these are more social norms than Jewish law.
As for myself, I would not recommend enlistment, but not because of a halakhic prohibition. I think national service can make a contribution that is no less significant, and usually even greater. Still, national service also has quite a few problems in certain places.