It wasn't necessary for Google to disprove Damore's arguments, because they didn't fire him over the quality of his science, but rather due to the controversy a

It wasn't necessary for Google to disprove Damore's arguments, because they didn't fire him over the quality of his science, but rather due to the controversy arising from his claims, whether true or not. It's completely irrelevant to Google's interests whether his claims were unsupported by data, harmful [to society], or politically incorrect. None of those were the reason they fired him: they fired him because his claims attracted attention that could reflect negatively on Google.