> It's as if once we allow these facts into the argument,
Right, facts.
Most of the biological arguments are very touchy-feely. But .. we can see differences in MRI between gays and straights (or men and women, or some other divide du jour)! That's to be expected. Unless your equipment is broken. But the facts that patterns in the brain has established doesn't tell us anything how, or why, they developed.
Scan a professional piano player and compare with a regular person and you'll pick up patterns there as well. Is that some sort of argument that piano talent is innate? If hypothetically some statistical factor could be identified that is more prevalent among black people and piano player, does that mean black people are more suited to be piano players?
No, it does not. Yet when considering sex differences, and to some extent race differences, those are the kind of argument that goes for factual. I doubt it's the factual part that bothers people, but rather the logical hoops necessary for these argument to gain practical relevance for decisionmaking.
I can somehow relate to the tiredness your friend expressed. In some other areas where I have taken active part for the past decade or two, I still encounter the same arguments over and over again (for example why open source is by necessity non-innovative), and every person genuiney believe they came up with a new and important thought that other people needs to consider. Just a quick skim of the discourse in the relevant area would really go a long way of presenting them in a more informed way.
So it might not be the arguments themselves that are tiring but the repetitivesness with the way they are presented.