Again I fully agree.
Now let me say this. It seems that we agree on what gender and sex are, and on how gender dysphoria operate.
What I noticed is that the transgender community and its advocates conveniently confuse the definitions of sex and gender when it is opportune to a particular narrative. Notably, the narrative that considers "sex change" as not only a scientifically possible thing, a remedy to gender dysphoria, but also a normal or benign thing to do.
Case in point, the usage of nouns such as "man" and "woman". These terms always designated sexes, not gender. Gender roles evolved and changed throughout history in Western society, but those terms never strayed away from the sexes they designated. However, from what I've seen, the transgender community appears to defend vehemently the position that "transwomen" are women, and not just men that have what society deems as traditionally feminine psychological attributes (same goes for "transmen").
Another example: the recent article someone posted on this forum that showed someone getting fired from their job for stating that "only women give birth" . Here again, I notice how biological realities and social constructs are all of sudden conflated by the same people who pretend to possess a clear understanding of what sex and gender are.
It stands to reason, at least to me, that this confusion is not only dangerous to teach to kids as we see in this video, but also inefficient as a way to fight the mental illness that is gender dysphoria, for the reasons you and I evoked.
Telling a boy he can be a girl is factually false and won't solve gender dysphoria. One could argue it could cause some.
Telling a boy gender roles are traditional conceptions that are not universal laws is factually true, and a much better and honest way to fight gender dysphoria.
I learned about the difference between sex and gender briefly in school at 11, then briefly in high-school at 16, albeit not in America. It was enough and perfectly clear to me that yes, I'm a man, but cooking is not forbidden to me and that I didn't have to enjoy cars or the color blue to be what I am. I wish these simple and transparent lessons could be taught to children without lacing them with lies designed to cater to unfortunately mentally ill "transgenders".