On the flawed statistical reasoning behind Google memo

This article is reposted in spirt of Women in STEM day.

Back in 2017, a Google engineer named James Damore posted a document titled “Google’s Ideological Echo Chamber” to an internal online discussion group. He argued, and cited research about men and women have psychological differences that are a result of their underlying biology. Due to these differences, men are better suited to be Software Engineers than women. Google, however, is trying to create an engineering workforce with greater numbers of women than these differences can sustain, and it is hurting the company. The memo and Google's quick dismissal of Damore stirred fierce online debate and subsequent lawsuits.

There are quite a few sound refutations of the memo; The Economist noted the memo's cherry-picking nature and numerous studies that can disqualify his claims. Wired pointed out that we are far from reaching anything conclusive with the current state of evolutionary biology and psychology. Aside from the aforementioned refutations, I would like to argue that the basic scientific reasoning behind the memo is flawed.

The memo's logic is that certain traits make a person a better software engineer, and men on average score slightly higher in those traits. The Economists dedicated a few paragraphs on the rebuttal of this claim, but let me first assume that such claim is valid. The memo continues with the argument that although the gender differences in the mean values on these traits are trivial, the characteristics of normal distribution makes men significantly more likely to become top coders.

The problem with this logic is that it is only valid if male and female have similar variability, or male has greater variability. Does male has greater variability in these traits? We don't really know; there are researches that supports greater male variability, greater female variability, and no variability difference. Yet the general consensus of these research seems to be that it depends on country and culture. 

Since the author attached a graph of two normal distributions, I also attached a graph to demonstrate that by abusing the exact same logic and data used by the memo, I can conclude that women have more potential to become top coders than men.