It quite easy to make wrong arguments in favor of positions that are true. If you think that an argument is good just because you think it's conclusion is true it's time to pause and reflect and look at a situation where the same structure of the argument would lead to a conclusion that's false.
Even if men and woman are on average equally qualified that doesn't mean that a specific subset is. For a hiring manager it's not important whether there's causation. Correlation in the data set is enough.
If you think that an argument is good just because you think its conclusion is true [...]
I agree, that's a very bad sign. On the other hand, there's nothing very alarming about thinking an argument is more persuasive when you agree with its premises. And often the premises and the conclusions are related to one another. That seems to me to be exactly the situation here.
Premise: There pretty clearly isn't an enormous cognitive difference between men and women that makes women much less competent at brainwork, so much less competent that a moderate amount...
I remember seeing a talk of the concept of privilege show up in the discussion thread on contrarian views.
Some discussion got started from "Feminism is a good thing. Privilege is real."
This is an article that presents some of those ideas in a way that might be approachable for LW.
http://curt-rice.com/quotas-microaggression-and-meritocracy/
One of the ideas I take out of this is that these issues can be examined as the result of unconscious cognitive bias. IE sexism isn't the result of any conscious thought, but can be the result as a failure mode where we don't rationality correctly in these social situations.
Of course a broad view of these issues exist, and many people have different ways of looking at these issues, but I think it would be good to focus on the case presented in this article rather than your other associations.