Let's start off by agreeing the Pay Gap is absolutely and completely misrepresented by most people. I'm NOT a feminist (I'm egalitarian), and the wage gap hurts men too. The social function and beliefs about men raising kids play a role in creating a wage gap in the first place. A friend literally just told me he wants to be a stay at home dad but he can't (because society would look down on that). Let's look at some data:

https://scholar.harvard.edu/files/bolotnyy/files/be_gendergap.pdf – Gender wage gap, this study finds that the gap is due to various job related factors in this specific occupation, not discrimination (NOT THAT THIS IS STILL NOT A PROBLEM TO CONSIDER)

https://www.pewsocialtrends.org/2020/01/30/womens-lead-in-skills-and-education-is-helping-narrow-the-gender-wage-gap/

https://www.aauw.org/app/uploads/2020/02/AAUW-2018-SimpleTruth-nsa.pdf

https://pubs.aeaweb.org/doi/pdf/10.1257/jel.20160995

https://www.epi.org/publication/what-is-the-gender-pay-gap-and-is-it-real/

https://www.hamiltonproject.org/assets/files/incomplete_progress_women_in_labor_force_NunnMumford.pdf

https://journalistsresource.org/economics/pay-gap/

Data shows that the pay gap for similar educated women, in similar occupations exist. This is due to a wide variety of factors, a large chunk of which are social beliefs about the roles and expectations of the gender in things like child raising, hours, etc. This is a bad thing for everyone on many levels.

The common representation of this is pretty bad (media is terrible), but ultimately, even as left wing male advocates, it is important we consider facts that don't agree with what might be some beliefs we hold closely and consider what the data says. I understand that the role of discrimination is not clarified perfectly (just like it isn't in studies of racial work discrimination either).

As much as we can argue about the job market being amoral, we have to recognize that the role of jobs and salaries in deciding freedom and opportunity is important. I'm a left wing socialist. The fact is that if women and men are being put in different positions by the market due to things like different working hours and flexibility, we can make changes on the social front (by being more egalitarian in division of responsibilities) and the market front (by incorporating policies that are good for all, like paternity leave, increasing and demanding flexibility for men, creating better policies regarding time off, childcare, reducing penalties, valuing less valued work, etc.)