Go to any post office in the US to see what is perhaps the most blatant and cruel example of institutionalized sexism in existence. And it's one which it may be impossible to eradicate. The equivalent exists in every country on the globe, almost certainly without exception (Israel is kind of a special case of which I'm aware and there may be others, perhaps not).
The gender discrimination I'm talking about is, of course, military service. The latest catch cry is "A Man's gotta do what a man's gotta do." The thing he's got to do is to sign up to be subjected to rigors and hardships which even prisoners these days are spared followed by the real risk (and often the certainty) of being sent to the most hellish places on Earth to be maimed and slaughtered with a brutality and cruelty which for the most part we spare animals and even insects.
But hey, a man's gotta do what a man's gotta do.
If war weren't horrible enough, the fact is that we may be stuck with it.
Some benighted folk can only see the superficial outward appearance that war happens because of religion or even economics or some other. These are almost certainly nothing more than superficial justifications and excuses. It's almost certainly more true to say that when there get to be too many people for the resources at hand and the technological ability to exploit them, societies are thrown into Malthusian conflict with one another in an exercise in reducing the total population. The most efficient way to deal with the problem is, rather than slaughtering large numbers of one's own population (although this is often done), sending large numbers of people from each side to murder one another. It's stupid and suicidal to send the women since they will produce the next generation (and very few men are required to help them do it), so the men, who also make up half of the population, are sent to in large part to be removed from the equation and give everybody left some breathing room. One ostensible objective is that one side or the other come out with fewer casualties and sort of wind up in the "dominant" position, but this is a very secondary consideration.
Another quandary at which many people shake their heads in tearful incomprehension is the tragedy of sending our youngest men, mere boys, really, in the very flower of their youth, to perish by the thousands in the trenches and on the battlefields. What a waste, a whole life thrown away, lost innocence, and so forth. In the Malthusian view, nothing could more obvious. Young men have their entire reproductive lives ahead of them, while an older man may well be past his and will probable die off soon, so it is the young men who have to go. If the objective were merely to win the war and come out on top, it would make sense to send the old men, more experienced, more of their lives behind them, already made their contribution to society, but this is apparently not the case. That older men have more political power than older men is probably mere window-dressing. In my own case, I am an older man and I have next to no political power, and no more than my peers or anybody else.
The "victor" will typically rape the conquered female population, imposing some of its genetic heritage upon the vanquished. Oh, by the way, surviving men in the vanquished country, combatants and non-combatants alike, are typically slaughtered as well. It's a man's life.
It's brutal and horrible for everybody, but by far and away so for the men.
Sexism and discrimination against women, although often terrible, I believe are perhaps without exception social constructs which can and will be eliminated. Men, and only men, being pressed into being soldiers may be something that we will never be able to end, certainly so long as we continue to allow overpopulation and war. In that sense, maybe religion is partly to blame after all, insofar as it oppose women's freedom to control their own reproduction, moreso than when it inveighs against the heathen and infidel. Women themselves must also be responsible when they do have the freedom to choose.
Even still, we may be stuck. As such, men must continue to be conditioned from a young age to be brutal, unfeeling killers. Whether we are at war or not, this does not have a positive impact on women, certainly not on men, on our economy, on our political institutions, or on our society in general.