This is, I think, the key. We can all recognize that there are REAL, average differences in interests between men and women, DEFINITELY driven by society/culture, and maybe by biology/genetics... BUT, this has absolutely no correlation with performance. If fewer women are, on average, interested in software engineering, this absolutely does NOT mean that women software engineers are, on average, worse at their jobs.
The error so many "Team-Damore" men make is that they zealously stand behind the argument that "Better-performing men are being overlooked in favor of worse-performing women/minorities." And yet there is absolutely no way to possibly back up that claim: can anyone clearly demonstrate over the course of a statistically significant number of hirings that most of the women candidates who were hired were A)chosen from a candidate pool that included at least one equivalently-or-more talented man; and B) that those men who were not picked would have been both better performing as individuals and better employees for the team/company as a whole? No. Nobody has shown this because it is, essentially, impossible to demonstrate. Citing studies of character traits or interests of men and women "on average" does absolutely nothing to support claims A and B. And so all these men end up doing is simply implying: "well, I BELIEVE that all these real women coworkers of mine are worse than the hypothetical male candidate that wasn't hired... on average." Which is clearly an insult to your existing coworkers and toxic to your work environment.