It is not stupid to generalize. It is nearly impossible to avoid generalization and should be a given that most people, when they generalize, are not referring to everyone. It is not necessary or possible to constantly be accurate. Of course what Schopenhauer says does not apply to all women. In a general sense he is correct. Women are given freedom and what do they do with it? They vote democrat, enroll in women's studies programs and whine about being objectified during slutwalks.
It has become quite clear to me why the wise men of old taught us that men should be the leaders in a society and in the home. Without stable men to lead, women become neurotic. I don't blame women for doing what comes naturally for them. I blame men for failing to be men. It's not women's fault, it is a crisis of manhood.
Ayn Rand explains it perfectly:
For a woman
qua woman, the essence of femininity is hero-worship—the desire to look up to man. “To look up” does not mean dependence, obedience or anything implying inferiority. It means an intense kind of admiration; and admiration is an emotion that can be experienced only by a person of strong character and independent value-judgments. A “clinging vine” type of woman is not an admirer, but an exploiter of men. Hero-worship is a demanding virtue: a woman has to be worthy of it and of the hero she worships.
This does not mean that a feminine woman feels or projects hero-worship for any and every individual man; as human beings, many of them may, in fact, be her inferiors. This does not mean that there is a romantic or sexual intention in her attitude toward all men; quite the contrary: the higher her view of masculinity, the more severely demanding her standards.
http://aynrandlexicon.com/lexicon/femininity.html