This is a world rebuilding after an epic shattering. A world in which _everyone_ is in mortal danger from giant spiders and rats and people who can fart out fireballs for real. Anyone who can hold a spear is going to be given a spear. Any country that chooses not to arm women out of some sense of obligation to being douchebags is going to do with a military capable force that's roughly half as large as the available pool of a group that is willing to put their women on the line.
More importantly than WIZARD HAT RATIONALE, this is a flavor option. It should either A) cost nothing or provide a benefit.
Equality. It makes sense.
edit: I'm trying to stay away from real world argumentation, because then I'd start getting irritated. But, pop growth reduction is actually beneficial in most societies so long as they're making the replacement rate -- which they don't need to do so long as they encourage immigration *COUGH* I'm looking at you Germany, stop with the haterade *COUGH*. Lower pop growth means fewer dependents per wage earner, meaning more resources available per dependent. Countries that have an incredibly high number of workers per dependent are experiencing something called a demographic dividend -- which provides a huge medium term boost to the economy. Perfect examples are the US with the Baby Boomers, China/India right now, Africa in the near future.
However, every demographic dividend comes with a demographic, well, I won't use the term I prefer here because it's not PC, but the closest equivalent would probably be bumpaddling. See, a demographic dividend also means a huge number of people in the same age category. And when that category marks the check box labeled Retirement, it imposes huuuuuuuge costs on their society. See Japan nowish, US and Europe in the upcoming years, China in the medium term. China is currently dealing with what's known as the 4:2:1 generation -- in other words, four grandparents, two parents, one kid. Once those parents and grandparents can no longer work, that kid is the only one supporting them unless the state gets involved in a far bigger way than it currently is in China. And since practically every family is in that situation, well, the only real option is massive immigration to keep the bills paid and the factories open. And where will that come from? Well, nowhere actually. Based on current trends in fertility, most of the world will be pop stable circa 2050. Things will be getting very interesting for China about then.
In most cases, population stability is immensely beneficial. It forces technological innovation -- because the only way to improve labor productivity is to improve techniques -- and keeps a lid on the cost of care for dependents. Plus, it means less rape of the environment! A win win!
Equality of sexual opportunity was huge. The post-WW2 boom in the US was literally built on the backs of women (and the devastation of practically every other industrialized nation on the planet, but we'll skip that). When you toss women out of the labor pool you're tossing out half the talent of society. That means less labor market competition, yes, but it also means less able people can take positions higher up the totem pole than they'd be able to in a truly competitive and open labor market.
In simple terms, given two equivalent economies where, ceteris paribus, one has no females in the labor market, the society with women as active participants in the labor market will economically dominate. Again in simple terms, given two economies where, ceteris paribus, one has a fluctuating dependency ratio and one of which has a stable drat, the stable drat economy will dominate.
So make the Egalitarian society 50% better in all ways and you'll be closer to the mark on what difference having females as labor market participants makes.