Do women and men have different brains?

Back when Lawrence H. Summers was president of Harvard and suggested that they did, the reaction was swift and merciless. Pundits branded him sexist. Faculty members deemed him a troglodyte. Alumni withheld donations.

But when Bruce Jenner said much the same thing in an April interview with Diane Sawyer, he was lionized for his bravery, even for his progressivism.

“My brain is much more female than it is male,” he told her, explaining how he knew that he was transgender.

Julie Doucet

This was the prelude to a new photo spread and interview in Vanity Fair that offered us a glimpse into Caitlyn Jenner’s idea of a woman: a cleavage-boosting corset, sultry poses, thick mascara and the prospect of regular “girls’ nights” of banter about hair and makeup. Ms. Jenner was greeted with even more thunderous applause. ESPN announced it would give Ms. Jenner an award for courage. President Obama also praised her. Not to be outdone, Chelsea Manning hopped on Ms. Jenner’s gender train on Twitter, gushing, “I am so much more aware of my emotions; much more sensitive emotionally (and physically).”

A part of me winced.

I have fought for many of my 68 years against efforts to put women — our brains, our hearts, our bodies, even our moods — into tidy boxes, to reduce us to hoary stereotypes. Suddenly, I find that many of the people I think of as being on my side — people who proudly call themselves progressive and fervently support the human need for self-determination — are buying into the notion that minor differences in male and female brains lead to major forks in the road and that some sort of gendered destiny is encoded in us.

That’s the kind of nonsense that was used to repress women for centuries. But the desire to support people like Ms. Jenner and their journey toward their truest selves has strangely and unwittingly brought it back.

People who haven’t lived their whole lives as women, whether Ms. Jenner or Mr. Summers, shouldn’t get to define us. That’s something men have been doing for much too long. And as much as I recognize and endorse the right of men to throw off the mantle of maleness, they cannot stake their claim to dignity as transgender people by trampling on mine as a woman.

Their truth is not my truth. Their female identities are not my female identity. They haven’t traveled through the world as women and been shaped by all that this entails. They haven’t suffered through business meetings with men talking to their breasts or woken up after sex terrified they’d forgotten to take their birth control pills the day before. They haven’t had to cope with the onset of their periods in the middle of a crowded subway, the humiliation of discovering that their male work partners’ checks were far larger than theirs, or the fear of being too weak to ward off rapists.

For me and many women, feminist and otherwise, one of the difficult parts of witnessing and wanting to rally behind the movement for transgender rights is the language that a growing number of trans individuals insist on, the notions of femininity that they’re articulating, and their disregard for the fact that being a woman means having accrued certain experiences, endured certain indignities and relished certain courtesies in a culture that reacted to you as one.

Brains are a good place to begin because one thing that science has learned about them is that they’re in fact shaped by experience, cultural and otherwise. The part of the brain that deals with navigation is enlarged in London taxi drivers, as is the region dealing with the movement of the fingers of the left hand in right-handed violinists.

“You can’t pick up a brain and say ‘that’s a girl’s brain’ or ‘that’s a boy’s brain,’ ” Gina Rippon, a neuroscientist at Britain’s Aston University, told The Telegraph last year. The differences between male and female brains are caused by the “drip, drip, drip” of the gendered environment, she said.

THE drip, drip, drip of Ms. Jenner’s experience included a hefty dose of male privilege few women could possibly imagine. While young “Bruiser,” as Bruce Jenner was called as a child, was being cheered on toward a university athletic scholarship, few female athletes could dare hope for such largess since universities offered little funding for women’s sports. When Mr. Jenner looked for a job to support himself during his training for the 1976 Olympics, he didn’t have to turn to the meager “Help Wanted – Female” ads in the newspapers, and he could get by on the $9,000 he earned annually, unlike young women whose median pay was little more than half that of men. Tall and strong, he never had to figure out how to walk streets safely at night.

Those are realities that shape women’s brains.

By defining womanhood the way he did to Ms. Sawyer, Mr. Jenner and the many advocates for transgender rights who take a similar tack ignore those realities. In the process, they undermine almost a century of hard-fought arguments that the very definition of female is a social construct that has subordinated us. And they undercut our efforts to change the circumstances we grew up with.

The “I was born in the wrong body” rhetoric favored by other trans people doesn’t work any better and is just as offensive, reducing us to our collective breasts and vaginas. Imagine the reaction if a young white man suddenly declared that he was trapped in the wrong body and, after using chemicals to change his skin pigmentation and crocheting his hair into twists, expected to be embraced by the black community.

Many women I know, of all ages and races, speak privately about how insulting we find the language trans activists use to explain themselves. After Mr. Jenner talked about his brain, one friend called it an outrage and asked in exasperation, “Is he saying that he’s bad at math, weeps during bad movies and is hard-wired for empathy?” After the release of the Vanity Fair photos of Ms. Jenner, Susan Ager, a Michigan journalist, wrote on her Facebook page, “I fully support Caitlyn Jenner, but I wish she hadn’t chosen to come out as a sex babe.”

For the most part, we bite our tongues and do not express the anger we openly and rightly heaped on Mr. Summers, put off by the mudslinging match that has broken out on the radical fringes of both the women’s and the trans movements over events limited to “women-born women,” access to bathrooms and who has suffered the greater persecution. The insult and outright fear that trans men and women live with is all too familiar to us, and a cruelly marginalized group’s battle for justice is something we instinctively want to rally behind.

But as the movement becomes mainstream, it’s growing harder to avoid asking pointed questions about the frequent attacks by some trans leaders on women’s right to define ourselves, our discourse and our bodies. After all, the trans movement isn’t simply echoing African-Americans, Chicanos, gays or women by demanding an end to the violence and discrimination, and to be treated with a full measure of respect. It’s demanding that women reconceptualize ourselves.

In January 2014, the actress Martha Plimpton, an abortion-rights advocate, sent out a tweet about a benefit for Texas abortion funding called “A Night of a Thousand Vaginas.” Suddenly, she was swamped by criticism for using the word “vagina.” “Given the constant genital policing, you can’t expect trans folks to feel included by an event title focused on a policed, binary genital,” responded @DrJaneChi.

WHEN Ms. Plimpton explained that she would continue to say “vagina” — and why shouldn’t she, given that without a vagina, there is no pregnancy or abortion? — her feed overflowed anew with indignation, Michelle Goldberg reported in The Nation. “So you’re really committed to doubling down on using a term that you’ve been told many times is exclusionary & harmful?” asked one blogger. Ms. Plimpton became, to use the new trans insult, a terf, which stands for “trans exclusionary radical feminist.”

In January, Project: Theatre at Mount Holyoke College, a self-described liberal arts college for women, canceled a performance of Eve Ensler’s iconic feminist play “The Vagina Monologues” because it offered an “extremely narrow perspective on what it means to be a woman,” explained Erin Murphy, the student group’s chairwoman.

Let me get this right: The word “vagina” is exclusionary and offers an extremely narrow perspective on womanhood, so the 3.5 billion of us who have vaginas, along with the trans people who want them, should describe ours with the politically correct terminology trans activists are pushing on us: “front hole” or “internal genitalia”?

Even the word “woman” has come under assault by some of the very people who claim the right to be considered women. The hashtags #StandWithTexasWomen, popularized after Wendy Davis, then a state senator, attempted to filibuster the Texas Legislature to prevent passage of a draconian anti-abortion law, and #WeTrustWomen, are also under attack since they, too, are exclusionary.

“Abortion rights and reproductive justice is not a women’s issue,” wrote Emmett Stoffer, one of many self-described transgender persons to blog on the topic. It is “a uterus owner’s issue.” Mr. Stoffer was referring to the possibility that a woman who is taking hormones or undergoing surgery to become a man, or who does not identify as a woman, can still have a uterus, become pregnant and need an abortion.

Accordingly, abortion rights groups are under pressure to modify their mission statements to omit the word woman, as Katha Pollitt recently reported in The Nation. Those who have given in, like the New York Abortion Access Fund, now offer their services to “people” and to “callers.” Fund Texas Women, which covers the travel and hotel expenses of abortion seekers with no nearby clinic, recently changed its name to Fund Texas Choice. “With a name like Fund Texas Women, we were publicly excluding trans people who needed to get an abortion but were not women,” the group explains on its website.

Women’s colleges are contorting themselves into knots to accommodate female students who consider themselves men, but usually not men who are living as women. Now these institutions, whose core mission is to cultivate female leaders, have student government and dormitory presidents who identify as males.

As Ruth Padawer reported in The New York Times Magazine last fall, Wellesley students are increasingly replacing the word “sisterhood” with “siblinghood,” and faculty members are confronted with complaints from trans students about their universal use of the pronoun she — although Wellesley rightly brags about its long history as the “world’s pre-eminent college for women.”

The landscape that’s being mapped and the language that comes with it are impossible to understand and just as hard to navigate. The most theory-bound of the trans activists say that there are no paradoxes here, and that anyone who believes there are is clinging to a binary view of gender that’s hopelessly antiquated. Yet Ms. Jenner and Ms. Manning, to mention just two, expect to be called women even as the abortion providers are being told that using that term is discriminatory. So are those who have transitioned from men the only “legitimate” women left?

Women like me are not lost in false paradoxes; we were smashing binary views of male and female well before most Americans had ever heard the word “transgender” or used the word “binary” as an adjective. Because we did, and continue to do so, thousands of women once confined to jobs as secretaries, beauticians or flight attendants now work as welders, mechanics and pilots. It’s why our daughters play with trains and trucks as well as dolls, and why most of us feel free to wear skirts and heels on Tuesday and bluejeans on Friday.

In fact, it’s hard to believe that this hard-won loosening of gender constraints for women isn’t at least a partial explanation for why three times as many gender reassignment surgeries are performed on men. Men are, comparatively speaking, more bound, even strangled, by gender stereotyping.

The struggle to move beyond such stereotypes is far from over, and trans activists could be women’s natural allies moving forward. So long as humans produce X and Y chromosomes that lead to the development of penises and vaginas, almost all of us will be “assigned” genders at birth. But what we do with those genders — the roles we assign ourselves, and each other, based on them — is almost entirely mutable.

If that’s the ultimate message of the mainstream of the trans community, we’ll happily, lovingly welcome them to the fight to create space for everyone to express him-, her- or, in gender neutral parlance, hir-self without being coerced by gendered expectations. But undermining women’s identities, and silencing, erasing or renaming our experiences, aren’t necessary to that struggle.

Bruce Jenner told Ms. Sawyer that what he looked forward to most in his transition was the chance to wear nail polish, not for a furtive, fugitive instant, but until it chips off. I want that for Bruce, now Caitlyn, too. But I also want her to remember: Nail polish does not a woman make.