Reddit reviews Modern Labor Economics: Theory and Public Policy (12th Edition)
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If I can explain, your reconsideration of the talking points is because of your misunderstanding of a confounding variable. It appears that the fraction of men and women in a field is causal, but in reality, it is not the cause of the wage gap.
The poster above gave a glib answer to why there is a wage gap, " The pay gap exists because women take lesser paying jobs." The reality is there are many reasons why women are paid less that can be explained using a human capital theory of compensation.
A regression analysis might look something like this:
Pay = aYearsExp + bContinuousExp + cEducationLevel + dHoursWorkedperWeek + eNumberofJobs + fRiskofJob + g
Men are more likely to have more experience as they have a higher labor force participation rate, which correlates with higher pay. They're also more likely to stay continuously working, mostly because women take a gap when they have kids. Women tend to be more educated these days, which correlates with higher pay, but not in the fields they choose, this has to be controlled for using stats methods.
Hours worked per week matters because typically overtime pay is higher than regular pay and men work longer hours on average.
Number of jobs matters because women are more likely to do part time work at more than one place, which grants neither overtime nor as much experience at a given job.
Risk of job matters, it's been found that once you control for other factors, a higher risk of death is implicit. Lumberjacks, compared to other blue collar jobs, when you control for factors get a slight boost. Since women don't face death at work, they don't get this boost.
Lastly, an unknown quantity G that can't be explained by the model. This is just a rough multi-regression of why the wage gap exists but I can promise you among labor economists, about 97% of the gap can be explained by standard human capital models.
Source, MA in Labor Economics.
https://www.amazon.com/Modern-Labor-Economics-International-Student/dp/0133462781
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