As he opened an archive centre at St John’s College, yesterday, I’m sure the Duke of Cambridge talked about many things. The weather, the price of petrol, what on earth is going on with X Factor these days. All the important things.

He also discussed his children. Nothing so odd there. But Master of the College, Professor Christopher Dobson, reported William as having described George as “lively” and Charlotte as “lady-like”. And that really does seem quite odd.

Whatever his apparently extensive collection of sweater vests may suggest, I have absolutely no doubt that Prince George is, indeed, “very lively”. At two years old, I imagine him haring around Kensington Palace, pulling centuries-old family heirlooms out of cupboards, and attempting to use his baby sister as a real-life Baby Annabelle. That is his right as a toddler. Were Prince William to have described the kid as “studious” or “serious”, I would have had some cause for concern. “Lively” is exactly what he should be.

And, of course, anyone who has ever met or been a two-year-old knows exactly what is meant by “very lively” in this context. “Very lively” is William’s way of telling the nation that what he and Kate have on their hands, like every other parent with a bundle of joy that age, is verging on a demon child. In Parent Speak, “lively” falls into the same category as “spirited” or “little tyke”: things we say about children when really we think they’re little shits half the time.

It’s actually rather endearing to imagine Will and Kate collapsed in a heap on the floor of a drawing room somewhere, while “lively” little George goes at the 19th-century wallpaper with a pot of Crayolas. It’s nice to know that even heirs to the throne have to use the naughty step every once in a while.

So that I can understand. But what is odd about William’s words yesterday is his description of his daughter Charlotte: “lady-like”. At just over five months old, let me paint you a picture of what this baby’s days, in all likelihood, look like. There’s a lot of gurgling, pooing and burping. She finds CBeebies hilarious, and it would still be perfectly acceptable for her to take her food directly from the body of another human being.

I never really know what people mean when they say “lady-like”, but surely not that. Surely not going to the toilet, in your pants, in front of Peppa Pig. So it doesn’t really make sense for a baby. Does William not realise that his daughter could quite easily confuse his face with that of Mr Potato Head? Because she’s a baby – not a lady, not an adult.

Prince William happy with baby

But describing Princess Charlotte as “very lady-like” is actually even stranger than that. Because William’s words yesterday didn’t just show an alarming ignorance of the mental and physical capacities of an infant; they also said a lot about the way we gender children.

George and Charlotte, at this stage in their lives, are doing exactly what all children their ages should be doing. George is causing chaos at Kensington Palace now, as Charlotte will later. And Charlotte is burping to order, just as George once did. They have no concept of boy things, girl things – just kid things, fun things, dangerous things they really want to touch.

Yet Prince William described them as almost polar opposites: “lively” and “lady-like”. Because, as an adult, fully immersed in and aware of a society riddled with gender stereotypes, he decided to play along. And thus, George grows up knowing that he can run and have fun and be “lively”, and Charlotte grows up thinking she must be quiet, polite and “lady-like”.