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It appears that the problem here is not as much the inherent badness of one worldview or another, but that the respective ideas are mismatched. For example: if one is to maintain that a woman does belong at home, then simultaneously one MUST require a man to be unable to divorce her. If a man is free to divorce his wife whenever he so pleases (or, to be fair, she is free to divorce him), then by all means, a woman should be (for her own safety) interested in getting a career that pays. This is logic, I'm aware that reality is much more complex, but after all, one of the reasons the patriarchy lingered so long is because, while women were restricted to the profession of a homemaker (or something that resembled it), the family was much harder to dissolve through divorce. Therein lies security, folks, and what people want most of all is security, isn't it?
The point of the article, as I see it, is that contrary to what Brooks says, it's far more dangerous for women, financially, to NOT have a career outside of the family, because it's so easy for them to be left high and dry when their husband tires of them. On the other hand, it's more dangerous for MEN to be married to a woman with a career, because... what if she tires of HIM? If she earns more than he does and leaves him, HE takes the financial hit. Columbo is full of stories where a hapless guy kills the wealthy woman he's courting or married to because somehow he's in financial trouble and she's not bailing him out anymore. THAT is why men are threatened by women who have better careers than them. It's not logical or anything to condone, it is what it is.
You know what, though? It would be SO much easier if nobody told anybody what they SHOULD or SHOULD NOT do. This world is far too complex for blanket statements.