If I were a computer engineer struggling in Google's male-dominated culture and woke up one morning to read a treatise by a male colleague arguing that innate biological differences between the sexes — not sexism — were to blame for the company's gender gap, I would be pretty damn pissed. But that wouldn't mean that my colleague was wrong — nor would it mean that Google's CEO was out of line in firing him.

All of that might sound contradictory. But it's not: The dilemma of the Google memo is that all sides have a point.

One would have to be pretty cynical to pooh-pooh the steady stream of reports that Silicon Valley — 80 percent male — is rife with sexism. Accusations of sexual harassment are frequent. Earlier this month, two startup investors were forced to resign after multiple allegations of sexual misconduct. But more than overt sexual advances, the bigger problem is the casual discrimination that stems not from an old-fashioned disdain toward women but a greater comfort level with the male, computer-nerd way of doing things that makes it difficult for women to flourish. On top of this, women are actively discouraged from speaking out through explicit non-disparagement clauses in sexual harassment settlements, or fear of retaliation or being branded as whiners not tough enough to handle it.

In the wake of all this, when a man comes along and pens a memo, titled "Google's Ideological Echo Chamber," complaining that the company's PC culture is preventing him from openly speaking out, it would be understandably galling. But that doesn't mean that he is simply wrong, at least in his central claim that sexism may not be the main cause of the tech gender gap and that aggressive diversity hiring can't completely cure it.

For starters, there is compelling scientific evidence that men and women do indeed have different cognitive endowments and personality traits. Contrary to feminist orthodoxy, men and women are different. We are not all born totally tabula rasa and then imprinted with socially constructed gender roles. Indeed, as blogger Scott Alexander points out in his superb examination of the gender differences literature, although both sexes have identical math abilities — at least as it relates to applied disciplines like computers — they show significant differences in mechanical reasoning (on which men on average score better) and verbal reasoning (on which women on average score better). Furthermore, women who are good at math also tend to have superior verbal skills, but men don't. However, the biggest differences between the sexes are not in their abilities but their inclinations: On average, men prefer to work with physical objects and women with people.

Now, even though almost half of undergrad math majors in America are women, they are still underrepresented in the tech sector. Some of this is sexism in the tech industry, no doubt. But plenty of women simply prefer to use their math prowess in teaching or other fields that involve people rather than machines. Or they give up math for more language-oriented professions. Or they opt out of the workforce completely or partially to raise families and strike a better work-life balance, a phenomenon that Lisa Belkin brilliantly reported in her New York Times piece, "The Opt Out Revolution," 14 years ago.

Ironically, Alexander points out, non-Western countries where feminism has made less progress in eliminating sexist stereotypes actually have more gender parity in technical fields than the West. In America, 26 percent of women enroll in computer classes. That is in line with: Sweden —30 percent; New Zealand — 20 percent; and Canada — 24 percent. But it's a whole lot less than: Thailand— 55 percent; Guyana — 54 percent; Malaysia — 51 percent; Iran and Zimbabwe — 41 percent.

Why is that? My guess is that when women are freed from the need to work for mere material survival and the forced drudgery of household chores, consulting instead their own inner capacities and desires to determine their professional destiny, technological fields sometimes lose their allure. In this, feminism has played a crucial role in liberating women from stultifying conventions and allowing them to fulfill their real needs. So if feminists would quit fixating on raw bean counting, they could perhaps start celebrating — instead of lamenting — that women's career choices don't exactly mirror men's.

But just because many women are more inclined toward non-tech fields doesn't mean that tech companies such as Google shouldn't make special efforts to pursue them.

There are many reasons other than political correctness — solid business reasons! — for Google to try and deal aggressively with the endemic sexism in its ranks and remove at least some of the cultural barriers that may be preventing capable women from jumping on board. Making socially obtuse male employees sensitive to what they might be doing to inadvertently turn women away is not exactly akin to sending them to Soviet re-education camp. The gender gap may never be closed — but it could be narrowed.

This is what the author of the memo failed to fully grasp in his single-minded insistence on exposing the difficulty that the differential cognitive inclinations of men and women pose for the company's diversity policies (although he emphatically did not say that women don't have the technical chops to rise to top ranks, as many liberals are accusing him of doing). Keeping him on would have made him a liability for Google's recruitment efforts, which is why Google CEO Sundar Pichai was not simply succumbing to the PC mob in firing him (as many conservatives are accusing him of doing). How do you keep on the rolls a person who has alienated a chunk of his fellow workers? If Google was at fault, it is in pretending that it was interested in open dialogue and discussion without drawing clear limits in advance.

Sometimes, it is possible for every side in a dispute to be partly right and partly wrong. Unfortunately, the furious culture war this memo has triggered is causing each side to focus on its opponents' "wrong" and ignore the "right."