Look at this bloodlessly, as you would a coding problem. Do you honestly think women and men are psychologically identical on every economically relevant metric, in capabilities and/or preferences? What would the world look like if this were true? What would it look like if it were not?
That's not what is meant by wage gap, you have been (intentionally) deceived. The gap only works if you do NOT account for things like "doing the same job".
Are you somehow personally slighted by this? every single wage gap "report" or debate is all about median/avg, not actual same job/title/responsibilities.