In that case I agree, the initial hypothetical is wrong because it isn't about same job/position pay, it is about likelihood to get promoted to a higher paying

In that case I agree, the initial hypothetical is wrong because it isn't about same job/position pay, it is about likelihood to get promoted to a higher paying position. It is about women being stuck in the same position, while men are more likely to get to the next level. From my reading of your post, it appeared you were arguing that the pay gap wasn't a thing at all. It is a common talking point, which is the reason for my (and maybe others) confusion. Anyway it seems it was a bad reading on my part. Unfortunately, the language we're using is a bit too loose to be accurate. Equivalently qualified isn't a stand in for equivalently competent. If women are less likely to get promoted, they therefore are less likely to have as many qualifications as men. This is an externality you would have to deal with, it would lead you to actually pick less qualified women to hire into promotions because there's a higher chance that they were passed over in favor of a man.