Circular thinking fail on her part.
Bodies are sexed, yes.
What makes any characteristic male or female?
The fact that it ONLY relates to ONE SEX.
Penises. Ovaries. They can be reliably described as male or female.
When is a characteristic NOT reliably described as male or female? When it occurs in BOTH SEXES. Even if it skews towards being more prevalent in one sex. It still cannot be described as male or female.
Exclusive to one sex? Label it male or female.
Present in both sexes? Don't.
Substitute 'gender' for height, or for colour blindness, or for weight.
A person who is 5'8" has a male height.
A person who is colourblind has a male condition.
A person who is 15 stones has a male weight.
A person with hypothyroidism has a female disease.
A person who recovers from Covid-19 has a female immune system.
It sounds stupid, obviously, because it is. These characteristics and conditions are found in both sexes.
Yes, they SKEW towards one sex.
But, noting that they are more prevalent in one sex or the other doesn't render them male or female.
The exact same principle applies to 'brain gender'.
Unless you are Deborah Soh, et al.
In which case you look at a trait, like, ability to parallel park, or load a dishwasher. And you determine that this ability, despite being easily observable in BOTH sexes, skews towards one sex more than the other and suddenly you gender-render it.
It's a logic fail, a false labelling.
Soh wouldn't take any other trait, like height, weight, or disease propensity and conclude - this skews 60:40, or 80:20, or 95:5 towards one sex so now it's literally labelled MALE or FEMALE because of a skew.
5'7" is a male height, so you, lady, have a male height.
Hypothyroidism is a female disease. You have a female disease, Mr Smith.
But she WILL do that with ability to play chess, or choose nursing, or any other skewed personality or brain aptitude.
It's simply an unacknowledged bias she has.
If it is exclusive to a sex, it can be labelled male or female.
If it is present in both sexes, even if it is more prevalent in one, it cannot.
(And none of that even begins to address her demonstrably false conclusion that "I observe a skewed trait - it must be innate".
"I see it, therefore I know what caused it" does not follow logically)