I think the questions of the OP are fair and need to be answered. Who can see the current liberal drift of the FSSPX and not realise that worldly "values" are indeed transforming the minds of Traditional Catholics ? Was this not exactly what occurred in the 1940s and 1950s, for which Our Lord spat the bulk of Catholics out of His mouth by taking away the Church from them ? Catholic life and the Kingship of Christ do rely on lay professionals, it is true (unless one believes that Catholic governments have no immediate need for jurists, diplomats, and civil engineers, which is quite a difficult position to argue). That being said, the rights of the Sacred Royalty of the meek and humble Heart of Jesus are not served by women being devoted to men's business in the public social world and neglecting their duties at home in service to their husbands and children. The Catholic City is directly built and guarded by men; it always has been and always will be. Those who propose otherwise would try to establish disorder in the family in order to build order in society, which is absurd.
Now, let's say a woman is skilled in music or languages or has an interest in history and philosophy or even, perhaps, mathematics. She argues (or rather her soft father with little understanding of natural theology argues) that she needs to develop these talents through formal disciplinary instruction in order to better educate her children.
First, if she is pursuing a career or higher education, she is not in her children's life as she ought to be in the first place and is likely bringing a lot of personal baggage and perhaps financial debt into a marriage. This has the additional effect of damaging her relationship with her would-be husband, since he will have to deal with a proud "back-seat driver" insisting on her own "accomplishments" being a sufficient foundation for her to habitually and systematically question his judgment and leadership/lordship. Strike one.
Second, if she is insistent on the necessity of learning these things to a professional level in order to educate her children, she seems to therefore imagine that she will replace, in her children's development, these institutions of higher education that she claims are necessary for full development in the first place. If her children can rely on her own skill and knowledge rather than on formal educational institutions, she has undermined her own argument regarding the necessity of formal educational institutions. If learning outside of these institutions is good enough for her children, it's good enough for her as well. Strike two.
Third, if she believes that she is disobeying God by not cultivating her talents to a professional level, she should seriously question what exactly the role of a wife and mother is. If she does have personal talents to contribute to a family, these will manifest themselves within her state in life as being first and foremost a wife and mother. That is to say, her primary understanding of her duty of state should derive from her immediate vocation. Her understanding of her personal talents and their significance ought to be formed upon this foundation, being a contingent logical step. Now, a woman's development of her personal career or talents at a professional level and then getting married afterwards belies a misunderstanding of the duties of a wife and mother, as well as a fundamental misunderstanding of femininity and social life. She would be disobeying God's law in the order of nature in order to attempt to serve God through developing her personal natural endowments. That is to say, she would be disobeying God in order to obey God, which is absurd. Strike three.
There does not seem to be any reason for this change in father's attitudes about their daughters except simple vanity. The women eat it up because women are naturally and uniquely vain about their self-worth since the Fall and are susceptible to internalising other's standards. A father who pushes this line of reasoning onto his daughter's will likely create little zealots for his cause of personal vainglory. This makes sense if we consider the instincts a wife and mother has to loyalty to a group, to protect her house and her children, etc. But these liberal fathers who push the soft feminist line to their daughters pervert, rather than sublimate, their daughters' womanly instincts. A woman's healthy pride in her natural community is inverted into a vicious pride in her self. Her loyalty and devotion are twisted into vanity and insecurity.