You seriously think it is okay for girls to be taught that it is their job to cook and clean for men, to produce babies for them, and to only take part in careers that are traditionally low paid, lower respect, and often require little education? And meanwhile men should be encouraged to take up any career that they like, to take up intellectual pursuits, and to "take care of women" by providing the income for the 20+ children they are required to carry and bear?

Because that is the sense I get from this family and others that insist on "traditional" (i.e. sexist) gender roles.
Perhaps what's wrong with the traditional roles is that they are completely made up by society and horribly detrimental and disrespectful to women. There is nothing about having a ****** that makes women better able to cook or clean and nothing about having a ***** that makes men better able to be scholars or work on a car. That's why throughout history people have had to make up so many crack-pot rationalizations for these roles--"Oh women can't be allowed education because it will make their uteruses wander" or "Oh, we can't ask men to do their fair share of cleaning because that would be an insult to their masculinity."
Besides the obvious detrimental affects that traditional gender roles have had on women for hundreds of years (keeping them uneducated, financially dependent on men, having no power in society, etc) there is a lot of recent research showing other kinds of problems with traditional gender attitudes. Amongst other things strong adherence and belief in traditional gender roles is correlated with high levels of homophobia, low levels of intimacy, and most disturbingly strong belief in traditional gender roles has been shown to be a very reliable predictor of attitudes which downplay the seriousness of violence against women in intimate relationships and/or have an attitude of blame towards the female victim.
So really the question is--why in the heck would ANYONE support traditional gender roles when they have been nothing but detrimental to women?