It's not a lie, pronouns are based on gender in pretty much every language on earth.
Why do you keep doing this, jj1968?
Only one in four languages on the planet are gendered, that is they use grammatical gender, an organisational system which requires that all adjectives, pronouns, articles and verbs are inclined to match the grammatical gender of the noun.
Some languages, like English, no longer have a grammatical gender at all, others never used this organisational system at all. While they may use personal pronouns all the same, these are always based either on sex or on grammatical gender.
But grammatical gender has nothing to do with the social concept of gender. In some languages grammatical gender depends on the sex of the living organism referred to, in others it doesn't. Some languages sort all nouns into male and female, always corresponding to sex in living organisms, some male, female, neuter, some animate and inanimate, other have male animate, male inanimate, female animate and female inanimate. (And a number of other options.)
In some languages, like German, you'll find that the Genus (grammatical gender) usually but not always matches the Sexus (biological sex) of living organisms.
But even where it doesn't, like with the example of Mädchen for girl mentioned above by OldCrone which has as a Genus Neutrum (neuter) even though the Sexus of a girl is female, where the referrent (the actual girl) is known, named or visible, it is actually much more common to use the ungrammatical she and all declined forms thereof even though das Mädchen requires es.
Because personal pronouns are based on sex in German, they can override the rules in common usage.
Moreover, many languages do not use personal pronouns at all, instead preferring demonstratives (so it's not she for girl but that instead). German actually has both, but it's considered quite rude to say die or der instead of sie or er for she and her.
Of course, one in three humans living on this planet speak languages that do not have third person pronouns or use third person pronouns that do not distinguish between the sexes in using them. Everyone is a form of they.
Which is why it's very common for speakers of Finnish, Chinese, Persian, Yoruba, Swahili, Maori or Hindi and Urdu (to name but a few of many hundreds of languages) to use he and she interchangeably when they first learn a language with third person pronouns that reflect the sexes.
In English then, the language the BBC is talking about, third person pronouns are based on sex. So it's completely wrong to claim the decision as to whether he or she is used is based on whether the person referred to conforms to the sex stereotypes and sex role stereotypes associated with one or the other sex.
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I can't help thinking that a little Bitesize lesson on international pronoun usage might be far more beneficial for our kids than this coercive one demanding kindness. It could teach them that not everyone does things the same way without labelling those alternative approaches as wrong, unkind, unfair, hateful or exclusionary.