When I was four, my role model was a small cartoon mongrel dog with a formidable talent for swordsmanship. Or swordswomanship, because I was convinced that Dogtanian (of Dogtanian and the Three Muskehounds) was a girl. My reasoning went like this: I am the most important person in the world and a girl, therefore the most important person in my favourite cartoon must also be a girl. And many happy games of Muskehounds were played by me, in my dungarees, oblivious to the unlikelihood of a children’s cartoon having a female lead in the first place, let alone giving that female lead the lovely Juliette as a romantic interest.

Eventually I realised my mistake, decided it was unfair that women never got to be action heroes, and grew up to be a feminist with the Alien films on Blu-ray. But it could all have gone another way. On Radio 4’s iPM this week, the mother of a 10-year-old called Leo explained that one of the reasons she knew her female child must be either a boy or non-binary was that Leo’s fictional idols were always male: Peter Pan, Iron Man, Wolverine.

Another piece of evidence was that Leo prefers pirates over princesses as a birthday party theme. And then there were the Barbies that Leo never played with. All of this, according to Leo’s mum, showed that Leo couldn’t really be a girl but must instead be either “male mind who happened to be born in a female body” or (in the family’s current favoured explanation) “a non-binary mind who happened to be born in a female body.”

The implication of all this is, of course, that a real girl – one with a “female mind in a female body” – would have rejected the superheroes, worshipped the fashion dolls, and unambiguously preferred crowns to cutlasses. Now, I cannot say whether Leo’s parents’ chosen course will prove to be good or bad over time. About 80% of children with gender dysphoria ultimately desist (that is, they decide they are happy in their body without hormonal or surgical alterations to to their sexual characteristics), and Leo’s mother sounds open to the idea that Leo could eventually be one of them.

But what I can say is the the terms Leo’s mother uses to explain the gender of her child can be construed as sexist. Last week the Science Museum responded to criticism of its Who Am I? gallery, which features a quiz to test the “sex” of your brain. A male brain, according to the quiz, is good at three-dimensional reasoning and rotation; a female one is distinguished by good memory and a sensitivity to subtle details. The accompanying visuals use pink for female and blue for male, following the grammar of gender that says princesses are pink and pirates are blue.

When I took the test, I came out as equally male and female – as well I might, because the idea that human sexual dimorphism is expressed in sharply contrasting aptitudes is, kindly, bunk. Even with a trait such as spatial reasoning, one of the few for which research has shown a consistent male advantage, we’re still talking about a difference in distribution rather than an absolute divergence of ability. In other words: if you tried to work out someone’s sex on the basis of their spatial reasoning test results, you’d still do little better than by guessing.

So why is brainsex lambasted when it comes from the Science Museum, but embraced as the height of liberal thinking when it’s used to identify children as trans? Leo’s mum is far from alone in this. A CBBC documentary from 2014 about a 13-year-old transboy (also called Leo) used images of pink brains in blue bodies and blue brains in pink bodies to explain the concept of transgender. In the documentary, the mother explains that she knew her daughter was really a son when Leo wanted short hair and showed a preference for “boys’ toys”. Or there’s the father who wrote in the Chicago Tribune that he realised his six-year-old male child was actually a daughter after the child rejected blue walls and dinosaurs for dresses and princesses.

Accounts of trans children consistently return to these stereotypes. Long hair or short hair. Trousers or frocks. Blue or pink. Children’s preferences are filtered through an adult rubric of gender and used to decide what sex they “really” are, despite the fact that we should know by now that sex is nothing more or less than our bodies. Our sex is a fundamental fact of who we are and how we are treated, but its ultimate truth is not decided by where we fall between the rigidly maintained domains of pink and blue. And thank goodness, because as much as I liked being a cartoon dog, I’m glad I know I’m a female human.