Time to dig this back up again, I guess:

There literally is no gender "wage gap". Firstly, the "wage gap" is a misnomer for the "earnings gap" (using the correct term makes it more clear that the difference is in average overall earning, not in the pay received per hour of the same work), and assuming whatever gap there is is caused by sexism is literally the same logic as the creationist's 'god of the gaps' argument re the fossil record; with that argument, creationists say X couldn't possibly have evolved into Y, that God was involved. Then when a transitional fossil Z between X and Y is found, the creationist says that God's influence must actually be between X and Z, and Z and Y. And so on ad infinitum, creating a situation where the creationist will always find a way to convince themselves that they're correct, despite the ever-increasing amount of evidence against them.

When it comes to the earnings gap, the actual gap that exists, the cause is assumed to be sexism/misogyny in the same way God is assumed to be how different species came about. But then as time goes on, research is done, and more and more of the gap is accounted for via factors that have nothing to do with discrimination/prejudice/etc., the argument changes to 'whatever gap remains unaccounted for, that must be the part caused by sexism/misogyny!"

That portion being due to sexism/misogyny is always based on pure assumption--there is zero hard evidence that instances of sexism (no one argues there is zero of it) comprise a statistically-significant portion (no one being intellectually honest would argue it's literally zero) of the earnings gap between men and women.

For anyone curious, here's a list of factors that contribute to the gender earnings gap, from the above link:

1. Men disproportionately gravitate towards higher paying occupations in technology and hard sciences (e.g., petroleum engineer).
2. Men disproportionately choose higher-risk, higher paying occupations with greater safety risks for occupational injuries and fatalities (e.g., oil field worker, roofer, and logging).
3. Men are more willing to work outdoors in uncomfortable, physically demanding work environments (construction, oil field workers, commercial fishing, logging).
4. Men are more willing than women to choose demanding, intense jobs where you can’t check out at the end of the work day (e.g., corporate attorney, senior White House staff).
5. Men select jobs with higher pay but with lower personal fulfillment (tax accountant).
6. Men select jobs with higher financial and emotional risks (e.g., venture capitalist).
7. Men are more willing than women to work the worst shifts during the worst hours.
8. Men often choose higher paying subfields (e.g., surgery and anesthesiology). <-- the primary reason for the misconception your oft-repeated joke is based on
9. Men are more willing to work in dirty or unpleasant environments with minimal human contact (e.g., prison guard, steel worker, truck drivers).
10. Men work longer hours per week than women on average.
11. Men more frequently than women invest in updating their skills with greater financial payoffs (e.g., master’s degree in computer technology vs. master’s degree in education).
12. Men are more likely than women to have more years of continuous experience in their current occupation.
13. Men are more likely than women to have more years of recent, uninterrupted experience with their current employer.
14. Men work more weeks during the year than women, on average.
15. Men are less likely than women to be absent from work (e.g., doctor’s visits, sick days, taking time off when children are sick, etc.).
16. Men are more willing than women to tolerate longer commute times.
17. Men are more willing to relocate, especially to undesirable locations at their company’s request.
18. Men are more willing than women, on average, to travel extensively on the job.
19. Men are more willing than women to take the risk of a variable income, e.g., to be paid by commission vs. a fixed salary.
20. Men often produce more output, e.g., scholarly research articles for university professors.

Note: None of those gaps above apply universally, but reflect overall gender differences that apply in general and on average.