Of course there are differences. Take a photo of women and men in any moment in time, and, apart from those matters related to reproductive physiology, you will find average differences in, say, fondness for romance novels, vampire movies, power tools, and fistfights. When I was a student, the differences of interest were in such skills as "finger dexterity", which explained why women were better at typing and cooking; women's "raging hormones", which made them unfit for serious work or political office; and "fear of success", which explained why there weren't more women in the professions. Interest in finger dexterity vanished when men got their clumsy paws on keyboards and kitchen utensils, and fear of success was trampled to death by the crush of women entering professional schools, once discrimination became illegal.

There is a benefit to having written about sex differences your whole professional life: you get perspective. When I was growing up, no American woman had ever been an astronaut, a rabbi, a general, a supreme court justice, or secretary of state. Women were barely blips on the radar in law, medicine, business, bartending, insurance, police, engineering, and politics. There were no women's WCs in the US Senate. Men and women cheerfully claimed they'd never work for a woman boss or vote for a woman. Of course, some things were better when I was young; PMS hadn't been invented.

There is also a disadvantage to having written about sex differences your whole professional life: it makes you feel awfully old, having to read, over and over and over and over, yet another incarnation of the view that men and women's brains differ in structure and function, differences that explain why women are allegedly better at empathy and talking than men and men are better at maths and science. You tip your hat to the current generation of scholars – notably Cordelia Fine, with Delusions of Gender and Rebecca Jordan-Young, with Brain Storm: The flaws in the science of sex differences – and you are grateful that they have taken up the cudgel as you sigh: "Here we go again."

To be sure, the biomedical revolution has produced stunning brain-imaging technologies, revelations about the human genome, and fascinating discoveries in behavioural genetics. Few psychological scientists are still fighting the nature-or-nurture war. I remember how angry feminist scholars were in the 1970s with sociologist Alice Rossi's "biopsychosocial" model of parenting – we wanted the "bio" part out of there. But that battle is over; it's nature and nurture. Few scientists (or parents) believe that any child can become anything with the right environment; the child's own genetic predispositions have something to do with his or her personality and interests.

But if biology itself is not the enemy in the study of gender, biological reductionism still is. The latest version even has a name, "neurosexism", the use of new technology or the language of neuroscience to support old prejudices and stereotypes. I've been following the studies of sex differences in the brain for two decades now, and have yet to be persuaded that they mean much, because the investigators perpetuate the same errors.

First, the very differences in behaviour they wish to explain are stereotypes – "women are more empathic than men" – and then any sex differences that turn up on a brain scan are invoked to explain them. But empathy is not a fixed trait, like eye colour. It varies with the situation. When social psychologists observe men and women in different situations where they are given the chance to behave empathically or not, sex differences evaporate. Are women more empathic than men in their dealings with enemies or strangers? Don't count on it.

Second, even when investigators discover a small brain difference – say, that in some women, both sides of the brain light up while they are doing a puzzle, whereas in most men's, only one side does – they often ignore the fine print: the more important finding that the sexes didn't differ in their actual test performance.

Third, brains are as idiosyncratic as fingerprints, shaped and sculpted by their owners' experiences over time; yet most people want to hear that brain structure determines behaviour, not that behaviour affects brain structure. In terms of brain function, the overlap between the sexes is greater than any average difference between them. Yet it's the differences that get the attention, publicity – and funding.

Here, then, is the irony: in developed nations, where women fight in battle and men change nappies, the sexes are becoming more alike in their roles, jobs, motivations, and values placed on work and family; yet efforts to pinpoint some essential difference in the brain continue. In the many countries in which women are completely ruled by men, where even the attempt to attend school puts them in peril of their lives, sex "differences" are at their greatest. Can brain scans explain the dazzling pace of progress in some nations and the brutal oppression of women in others?

Worldwide, the greatest predictor of women's advancement in science is the extent to which they have equal access to education and careers, not which half of their brains lights up when they are doing a maths puzzle. That is a finding that has not changed in my lifetime, and I doubt that all the brain-scan studies being done today will change it in the future.

• The University of Cambridge Centre for Gender Studies, in association with the Guardian and supported by Cambridge University Press, is organising a series of debates on gender and radical biomedical advances. Book tickets to the events here. This is part of a series of articles on Comment is free that will accompany the debates