Actually it's not a myth. Look up bureau of labor statistics. Women clearly make less than men. I feel something must be done to resolve compensation when controlling for skills, experience, etc, gender alone shouldn't result in lower pay.
Again, there is no difference in average hourly rate of wage. Men make more money than women because men (on average) work more hours a week as compared to women. Also men take fewer days off (on average). Thats the reason behind the mythical "wage gap". So, the correct term for it is "earnings gap".
There have been a bunch of studies of this, and the conclusions are pretty consistent: women aren't paid less for doing equal work, they're paid less because they end up doing less or lower-paid work once they have children, because they do a disproportionate share of the childcare.
This should still be fixed, but it means the fix is mostly about what happens at home, not what happens at work, which is much more difficult.
https://www.bls.gov/cps/cpsaat11.htm