Man, I really don't want to be a Damore apologist, but-
"that women were innately less qualified"
He never said that, though. If you have to grossly misrepresent his argument like that, you've demonstrated that you have no good faith retort and have lost the argument at the outset.
His paper was about on the average traits. That if you've split humans into various subsets -- for instance ethnicity, sex, age, etc -- each group has average and percentile traits on a variety of axes, whether it's aptitudes or intelligence spread (e.g. the variability hypothesis), musculature, long distance running, etc. These traits have negligible applicability to any individual person or subset, but if you're selecting from the whole set for exceptional extremes, you likely will get a set that doesn't demographically represent the whole.
NBA/NFL/NHL/MLB players. Nobel prize winners. Top mathematicians. Long distance runners. And so on.
Damore's mistake was that a) there was no value in publishing this, b) he is on the spectrum and didn't realize how dangerous this absolute statement of fact was.
You say that he had bad science, but then you link to a piece that says that it's "politically naive, and at worst dangerous". Which is precisely the sort of tired "but it isn't socially acceptable" sort of response that is just boorish and unproductive.
I get why Google fired him. They pretty much had to (though I would argue that he could have contested it as punishing his handicap). But for all his folly, when people have to misrepresent what he said, or do the "it's bad science because I don't like it"....meh.