Right, so, when we think about classical Western thought, the ideological machineries that explained why women were inferior to men were actually quite sophisticated. In Greco-Roman Antiquity, a woman released all the evils to the world (myth of Pandora); women were considered comparable to children in that they had no self-control over their rationality, emotions or sexuality, which meant that they needed to be controlled (thanks, Aristotle); and whereas man's duty was to be loyal and useful his homeland, woman's was to be loyal and useful to her husband. The Christian thought inherited similar themes, with Eve of course being the reason human kind bear mortal sin and Thomas Aquinas coming up with such great conversation-openers such as "woman is defective and misbegotten, for the active power of the male seed tends to the production of a perfect likeness in the masculine sex; while the production of a woman comes from defect in the active power..."
I'd be interested to hear, how women and femininity were conceptualized in the Asian intellectual tradition, seeing that women were (as I've understood) also considered inferior to men on the continent until modern times. Did e.g. Chinese imperial thinkers write treatises on women? Why did they think women were inferior to men? What was an ideal women like? Were there exceptions to the rule (like there were in the West) and some ancient authors who advocated more rights for women? Big topic, I know, but I'd welcome comments giving insights on individual authors just as much as big sweeps! Would love to hear from e.g. Japanese and Indian intellectual traditions as well.
Everything that follows is tied to Ming and Qing ideas on women within Confucianism. In your question and thoughts on Western ideology, you use the word ‘inferior.’ When talking about women’s roles in Imperial China from today’s perspective, it is easy to view women as ‘inferior’ to men. Traditional Confucianism, or Han teaching (儒汉), does place female roles under male roles. However, these roles were also heavily demarcated.
One concept that stands out is 「男外女內」. I have confidence in my academic Chinese, but was never good at translating. This idea places men in the ‘outer sphere’ where as women were in the ‘inner sphere.’ Unlike in lots of Western discourse, we tend not to use ‘public’ or ‘private’ spheres when discussing Chinese gender roles as the discourse is already provided to us.
A second concept that stands out is「男尊女卑」. This is to ‘respect’ men and have ‘modest’ women. In particular the character 卑 can mean both inferiority and modesty. These two phrases are often dotted about in how intellectuals discussed gender roles.
You mention those who advocated for women’s rights. In the late Qing dynasty a group of female writers called themselves 「閨房之秀」. Again, I cant translate this properly, but this group of female writers (poetry and articles) attempted to promote women to better understand the ‘outer’ sphere, in particular politics and definitions of a nation-state. Interestingly enough, the meaning of 閨房 is closely aligned with the aforementioned ‘women in the inner sphere’ attitude. In a sense, they were publicly affirming the female gender role.
Edit: It may be worth to note that heavily studied 梁启超 (Qichao Liang, a very very influential male late-Qing intellectual) ridiculed these women and their views, even though he often advocated for their rights. One of the reasons was their lack of education and lacking a serious demeanor.
At the beginning of your question, you ask WHY are women put in this position. Unfortunately, I don’t have all the information on that. However, these Confucian ideas may be closely aligned to early Buddhist views. In traditional Chinese Buddhism blood is viewed as a type of pollution. For example, Qing dynasty butchers did not put the seal/name of their shop on paper that wrapped meat. They feared their butchery would become polluted if it touched meat. Therefore, the menstrual cycle and childbirth were also connected to the idea of pollution. Since men do not possess these characteristics, it is easy to see why women were ‘inferior.’
Additionally, the act of childbirth and childrearing is intrinsic to the ‘inner’ sphere. These reproductive cycles are one reason why Chinese women were relegated to the ‘inner’ sphere. In turn, if your Confucian role is inner, then that leaves the outer for the male.
Edit: Sources 卓意雯，《清代臺灣婦女的生活》，臺北：自立晚報出版，1993。
李毓嵐，〈日治時期臺灣傳統文人的女性觀〉，《臺灣史研究》，第十六卷第一期（2009三月），頁87-129。
Mann, Susan and Yu-yin Cheng. Under Confucian Eyes: Writings on Gender in Chinese History, edited by Susan Mann and Yu-yin Cheng. Berkeley and Los Angeles: University of California Press, 2001.
Qian, Nanxiu, Grace S. Fong and Richard J. Smith. Different Worlds of Discourse: Transformations of Gender and Genre in Late Qing and Early Republican China, edited by Nanxiu Qian, Grace S. Fong, and Richard J. Smith, 1-25. Brill, Netherlands: Hotei Publishing, 2008.
There's an interplay at stake owing to Confucian values that might confuse a straightforward approach to the role of women. Filial piety meant that, in the imperial court, the Empress dowager often held considerable power over the incumbent Emperor, to the point where they effectively ruled the empire until their deaths. Many empress dowagers held de facto power, such as Dou of the Western Han, and Cixi of late Qing dynasty, while one, Wu Zetian, would openly declare herself "Emperor". Imperial court intrigue often featured concubines vying for the title of Empress and control of the throne through the naming of a crown prince.