Well, boys have words, willy and balls, and I imagine most know penis and testicles as well, and everyone knows what all those words mean. Willy especially is a "friendly" word that people aren't going to get upset about a child using. Boys never use the word willy to mean any bit of them that isn't a willy, same with balls.
Girls don't have this. They have flowers, and noonoos, and front bottoms, and vaginas (to mean the whole thing) and fairies, and all sorts of things. Many of these words would not be understood by someone not from that family / area of the country if the context was not very clear. Many of these words have other meanings too. To most people (around here) a vagina is a vagina and isn't used to mean "the whole thing" and so a situation like the OPs would be eyebrow raising as to all those people what that teacher said is nonsensical.
And all of this is because actually, most of the time, women's genitals and reproductive functions are (because history) rather unmentionable, because of associations with being unclean, unladylike, and so on.
I think it's a reasonable conversation to have.
And incidentally it was this post of yours I was writing about "As much as the terms I used. What differentiates vagina or clitoris from frenulum or epithelium?". And as I said, I don't think those terms are on a par at all, and females (and males for that matter!) damn well should know what a vagina and a clitoris are. Same as they should know what a penis and testicles are.