Why does the inferiorization of women help capitalism?

Your question suggests that limiting the rights or status of women in some way is good for capitalism. It's not.
We know that economic growth is lower and income inequality is greater in countries with fewer rights or lower status for women, compared to countries that treat women better. We know that the single greatest predictor of economic growth trends in the developing world is the percentage of women educated to high school level. We know, furthermore, that societies with greater respect for women have a better quality of life for everyone, as measured by incidence of infant mortality, life expectancy, and literacy.
Diversity is also good for business. Companies which treat women better have higher long-term growth rates, better profitability, and better working conditions than companies that don't treat women well.
So, it's not true that making or keeping women inferior to men is good for capitalism. In fact, the reverse is true. More power and status for women is good for capitalism.
http://hdr.undp.org/en/2018-update

https://fortune.com/2017/01/18/leadership-diversity-bottom-line-career-advice/

https://iwpr.org/publications/the-status-of-women-in-the-states-2015-full-report/