Consider Reardon, Kalogrides & Shores (2019). They found that even in districts where lower-performing groups had higher SES than Whites, they still tended to perform worse.
In this picture, 79% of the mean Black-White gap is independent of SES. At the metro level, 62% was.
It is a pernicious myth that test scores and achievement gaps are mere reflections of geography and that geography plays a major causal role in test scores.
The truth is that their association primarily reflects selection.
Greater Male Variability rarely makes for an adequate explanation of sex differences in performance.
One exception may be the number of papers published by academics.
If you remove the top 7.5% of men, there's no longer a gap!
The disciplines covered here were ones with relatively equal sex ratios: Education, Nursing & Caring Science, Psychology, Public Health, Sociology, and Social Work.
Because these are stats on professors, this means that if there's greater male variability, it's mostly right-tail
Despite this, the very highest-performing women actually outperformed the very highest-performing men on average, albeit slightly.
The percentiles in this image are for the combined group, so these findings coexist for composition reasons.
If men do more of the housework and child care, fertility rates will rise!
Men have been doing increasingly large shares of the housework and child care.
Fertility is lower than ever.
In fact, they're doing more in each generation, but fertility has continued to fall.
The original claim, that men's household work would buoy fertility, was based on cross-sectional data that was inappropriately given a causal interpretation.
The updated cross-sectional data is as useful, and it affords no assurances about the original idea.