I don't have to believe you- because I've seen it happen first-hand myself!! I've even assertively asked this question in meetings: "Folks, can we listen for a moment to what {name} has to say?" It is moronic to believe that 51 percent of the population doesn't have the potential to contribute 51 percent of the potentially innovative ideas of a societal whole.
I would go so far as to say that aside from efficient manufacturing and natural resource deposits, innovation (i.e. ideas) are the #1 driving factors for a nation's advanced economic growth. Assuming that you can exclude the potential intellectual contributions of large portions of your population from that resource pool is dooming yourself to failure.
When I look at nations which limit women's opportunities to contribute as equals by limiting education and working opportunities, I see nations that are at the very least 200 years behind nations which do not. In other words, even if they abruptly started allowing women to learn and work today, there will be roughly 200 years of negative cultural inertia they'll have to overcome before those nations catch up socially and therefore economically. Collectively you have to start looking at your nation’s cumulative intellectual output as an exportable resource.
It's a prime example where a particular culture, no matter how historic, can universally affect quality of life. Sometimes the culture "you know and grew up with" is a culture you need to rethink, even at the cost of nostalgia.