And why they could not?
Because women were meant to marry and raise children ASAP.
Now that this environmental/family/religious pressure is less and less important, more and more women 'contribute to the advancement of society'.
During the very religious Middle Ages, girls' schools were rare, and their education was quite limited, most of the time, to domestic arts.
The most educated women would end nuns in convents.
Schopenhauer understood the situation better then most, and his elucidations have become nearly prophetic in light of current trends. I don't have much too add to his excellent analysis.
Schopi wrote a lot of very interesting stuff, but also said that the woman is an animal with long hair and short-sighted. I wish you could explain this to Marie Curie-Skłodowska, Lise Meitner, Rosalind Franklin, Grace Murray Hopper, Erna Schneider Hoover, Rosa Parks (talking about obedient animals), and also Hatshepsut, Hildegard of Bingen, Catherine of Siena, Catherine II of Russia (unfortunately for Poland), etc.
This shows that women, when they have the means, ARE capable of achieving great things. And this is enough for me to disagree with Schopenhauer's slightly misogynic views on women.
Also, I don't believe in innatism. At birth, a baby is only biologically a male or a female. It will 'become' a male or a female during the first years of its life. I'm not saying there is no difference between men and women, only that these differences are not THAT significant. Some men hate football, some women love cars. Some men clean toilets, some women rule states. I honestly know very few animals that rule countries.
As to men being more intelligent than women, I found something interesting (;)).
So it is not that men are more intelligent than women, but that taller people are more intelligent than shorter people, but net of height women are more intelligent than men. Women who are 5'10" are on average more intelligent than men who are 5'10", and women who are 5'5" are on average more intelligent than men who are 5'5". But, more importantly, people who are 5'10" are significantly more intelligent than people who are 5'5", and most people who are 5'10" are men and most people who are 5'5" are women.
psychologytoday.com/blog/the-scientific-fundamentalist/200901/why-men-are-more-intelligent-women
Just found it worth reading. Although I already know Mr ZIMMY will not agree for some reason.