The pay gap isn't a single thing; it's a combination of factors:

1. Studies don't find that person XX and person XY actually get the same pay -- there is still a few % difference for identical jobs.
2. Person XY is still more likely to be promoted to job + 1 than person XX, thereby widening the gap.
3. When person XY or person XX is promoted, it's more likely that person XY2 will be hired to replace them than that person XX2 will.
4. Person XX2 is more likely to choose to go into a lower-paying field than person XY2 in the first place.

The typical antifeminist claim is that the first three factors don't exist, and the fourth factor -- that women choose lower-paying professions -- is entirely innate, and therefore not something we should care about.

The feminist claim is that the first three factors do exist, and that the fourth is due to the vast array of social pressures that push women away from higher-paying fields -- everything from "girls aren't good at math" to sexual harassment by professors to men wanting their wives to stay at home and raise children.

The antifeminist strawman is that we should pay women more for their jobs so that pay gap disappears even though women are doing less/less prestigious/less difficult work.

The actual feminist solution is that we, as a society, should work to eliminate or counteract the pressures that keep women from choosing higher-paying work.