First off, the author misrepresents the idea of patriarchy as a "conspiracy of men to subjugate women". That's not how I've heard how it's been defined. Patriarchy/kyriarchy, roughly put, is a series of assumptions and privileges provided to a segment of the population, often at the expense of everyone else.
It's not, as far as I can see, a conspiracy -- i.e. a secret plan hatched by a clandestine group that goes against a larger society's interests. You can have a pat/kyriarchy where each member acts on their own best interests, and yet the results of that unfairly disadvantage certain groups.
A good example of the kind of decentralised, mass-action that disenfranchises a particular social group or class can be found in Michael Young's coining of the word "meritocracy", and how, through the collective action of a group of self-interested actors, a particular social group can be disenfranchised or demoralised. It doesn't require secrets, it doesn't require conspiracies, as a matter of fact it just requires everyone acting to their own best interests.
Secondly, the author doesn't make a convincing argument that the fact that the reason why men get all the risk and all the reward is because of something innate, instead of a self-perpetuating social system that actively encourages one gender to risk it all and reap the rewards, while holding back the other gender to mediocrity and risk-free existences. The possibility is raised for a few sentences, and discarded, as if it's ridiculous, and it's obvious that the reasons are inherent.
Since the arguments in the rest of the post requires me to buy the above premise without conclusively eliminating social mores and non-innate possibilities, I didn't bother reading the rest of the article.
Incidentally, as a member of a nation that was born out of British Colonialism, the statement "the British Empire did a lot more good than harm" is a disgusting, privileged statement that really doesn't elicit much more than pitying contempt from me. Since of course we wouldn't have known what our lives would have been without John Company coming down to "civilise" our barbarian asses, obviously the only feelings we should be having is gratitude, especially since we owe our broken conception of race and ethnicity, our de-facto one-party rule since we gained independence from our Magnanimous Masters, our police force, more intent in beating down dissent and enforcing "public order" that is beneficial to only the ruling class and no one else, to organisations, concepts and social structures derived from British rule.
That's right; it was this or barbarism. Yeah, I hope it helps you sleep at night too, jerk.