We have taught Zoomer about their own body without using boy-girl labels. Zoomer understands that some girls have penises and some boys have vulvas
So what have they taught Zoomer about what the words "boy" and "girl" mean? What does Zoomer believe are the categories that these labels refer to?
How is Zoomer supposed to work out whether Zoomer is a "boy" or a "girl" in the absence of trusted adults who can delineate the specifics of these categories?
Kids can figure out pretty damned easily what sex category they're in even if you deny them a word for that category; most of them are exposed to the idea that undercarriages come in two distinct models pretty early on and Zoomer's no exception - Zoomer knows whether Zoomer has a body-with-vulva or a body-with-penis. All they've done is deny Zoomer access to the language the rest of the world uses to describe this.
We don't learn language by reading dictionaries. We learn it by listening to it; we figure out what each word means by hearing it used in context.
When Zoomer's out and about in the world, and sees some children described as "boys" and some children described as "girls", Zoomer knows these words do not refer to penis-bodies and vulva-bodies. Zoomer is then left with the job of inferring the meaning of these words from observation. What conclusion is Zoomer likely to draw about the categories these labels are applied to?
"Girl" = generally into skirts, makeup, dolls; unlikely to be into football; expected to maintain a higher standard of decorum at all times
"Boy" = generally into dirt and wrestling; allergic to skirts; shitty behaviour naturalised and handwaved
Zoomer then gets to decide which of these categories best fits Zoomer, and choose a label accordingly.
But Zoomer is being explicitly denied access to a comprehensive understanding of the labels Zoomer's being expected to eventually choose between. Zoomer is learning the stereotypes but not the sexed basis of them.
Zoomer cannot have an understanding of Zoomerself as having an identity that aligns with Zoomer's sex, unless Zoomer is taught what a sex actually is. Equally, Zoomer cannot have an identity that Zoomer feels doesn't align with Zoomer's sex. Because Zoomer is being taught that these mysterious amorphous identity categories of "boy" and "girl" are not linked to the "sex spectrum" in any way.
It's almost like they're trying to deny Zoomer the capacity to develop a cross-sex identity. Which looks a bit transphobic to me.