Why some people think women are inferior, and why they are wrong

I have been reading Angela Saini's new book, Inferior: How science got women wrong and the new research that's rewriting the story. It looks at all manner of preconceptions, received wisdom and scientific research around the general intersection of gender and science, from intelligence to emotion to behaviour to gender identity to education. It throws new light on old saws like "men are naturally more intelligent than women", "men's brains are bigger than women's", "men are analytical and women are empathetic", "nature is more important than nurture",  "men are promiscuous and undiscriminating, women are choosy and chaste", "the vast majority of science professors are male", etc.
En route, it throws up a bunch of interesting factoids:

• Married mothers of young children in the USA are about a third less likely to get tenure-track academic jobs than married fathers of young children. BUT ... unmarried childless women are actually 4% MORE likely to get those jobs than unmarried childless men.
• Although they typically get sicker more often, women are biologically better survivors than men, from their survival rates in childbirth early childhood (at least where equal healthcare is provided) to their significant advantage in longevity, and one reason may be their stronger autoimmune system, which in turn may be due to their need to host and nurture a foreign body during pregnancy and childbirth, and also the doubling up of many genes from the female XX chromosomes (as opposed the more heterogeneous male XY chromosomes).
• Only a small minority (around one in five) of pharmacology and physiology studies look at both genders, with about eight out of ten showing a male bias, despite increasing evidence that women's bodies, and particularly their hormones, often reacts differently to drugs and treatments.
• Although there is no statistical difference between the genders in "general intelligence (a measure taking into account intelligence, cognitive ability and mental ability), there is statistically more variability among men, meaning more men of extremely high intelligence and - to a much greater extent - more men of extremely low intelligence.
• The male propensity for traditionally male pursuits like sports, cars, construction, etc, may not be innate, but merely a function of the amount of stereotyped reinforcement at an early age from well-meaning and unaware parents.
• For decades it was maintained that, because women's brains were, on average, about five ounces lighter than the average man's (42ozs or 1,198g, as compared to 47ozs or 1,336g), women were that much less intelligent. It was only when it was revealed that the (male) founder of the Cornell Brain Collection himself had a brain about the size of the average woman, that it was admitted that brain weight and volume is actually proportionate to the size of the person, thus also explaining that elephants (which have brains weighing about 11lbs or 5kgs) are not more intelligent than humans.
• Desperate to find other physiological differences between male and female brains, other researchers have turned to: the fact that women's brains have 15-20% higher blood flow than men's; that women have a higher percentage of grey matter in their brains, while man have more white matter or connective tissues; that men have more connections within the hemispheres, while women have more connections between the hemispheres; etc, etc. But other studies have shown how hard (or rather easy but unjustifiable)  it is to draw sweeping conclusions from the even most detailed brain scans, and the academic pressure to publish something eye-catching on a hot-button topic.
• There is good evidence that biology and society are inextricably "entangled". For example, studies from the 1970s and 1980s showed that exceptional male mathematicians outnumbered females by as much as thirteen to one; more recent studies show this imbalance to be closer to four, three or even two to one, suggesting that this is not due to biological differences but to sociological and cultural differences that can change over time.
• "Mate guarding" - forcing a female to be sexually subservient and monogamous, even to the detriment of the species or group or the physical wellbeing of the female - is a common behaviour among many animals. The human equivalent can be seen in practices like female genital mutilation, breast ironing, foot binding, the use of menstrual huts, etc.

Ms. Saini's conclusion is that the physical sex differences in the brain (as well as behavioural and psychological differences) are actually minimal, and mainly a function of the relative sizes of men and women (and consequently of their brains). Those differences that have been shown in various studies over the decades are overblown, exaggerated or misinterpreted, often the result of over-zealous researchers on a mission to make their names as pioneers of the theory of sexual dimorophism of the brain (the names Ruben Gur and Simon Baron-Cohen come up regularly in this context). Ms. Saini (often based on the work of others before her) skewers study after revered study, pointing out inconsistencies, errors and bias.
There is, however, still a vocal and influential (and mainly male) movement that insists that the differences are real and significant. Tempers can become very hot in this contentious area of neuroscience, and there are reports of offensive, even threatening, emails making the rounds. New words like "neurosexism" and "neurofeminism" have been coined. New research in the area gets covered in major national newspapers, unlike most scientific studies, because it is seen as subject that many people are very interested in and touches us closely (we all have brains, we all have genders, we all have sons or daughters or fathers or mothers).
The jury, as they say, is still out. But, you have to ask, is it important? What is the justification for all this research? And, for that matter, who is paying for it?