"Well it could also be argued that the reason why more more men are in the army is because it’s a very dangerous job that requires long periods of time away from the home and women are needed to care for the children. If we lived in a completely equal society it could be the case that the duties of childcare were spread evenly between the sexes and therefore more women WOULD join the army. "
.....................Start at "very dangerous job"
add "that requires learning how to kill people and willing to be killed"
Then add "long hours away from home"
"therefore more women WOULD join the army."
Yes, it's possible, but would there still be more men in the army - that's the question. Not would more women join the army.
The scenario is eliminating all social stigma, conditions and barriers...therefore it can be assumed that more women will do masculine jobs because of no social stigma.
The question (again) is would there still be professions that are male dominated eg 50%+ in a social stigma/barrier less world