(just looking at heterosexuals as you are doing,) every time a man forms a relationship with a woman, a woman also forms a relationship with a man. So, "different outcomes" for men and women are bounded by the roughly equal numbers of men and women, and the number of single men will come out the same as the number of single women*, so any impact that introversion of either sex has will also play out in the other sex. So, if introverted women are getting more relationships than introverted men, then there a bunch of extroverted women who are not getting relationships.

*women tending to date men older than them and vice versa does mean that in an increasing population there might be more women in a particular dating pool than men than one would otherwise expect, but there might be negative feedback in the form of more pressure for age-reverse relationships to take up the slack

btw, this type of reasoning also applies to many other relationship canards like "men are more promiscuous than women", because no, not possible