I can see why a school would avoid using daughters for reasons that have nothing with gender, as others have already discussed.
The avoiding using girls part though, I can see why that could be called into question to at least understand why though I can also understand that the school may be in a difficult place on that depending on what's going on with their students and the area.
A school promoting the idea of misgendering as violence... yeah, I'd want more information on that, I don't like the idea of being taught someone can accidentally be violent or that other people not seeing us as we see ourselves is violence. Hurtful, sure, violent, no. Using misgendering to harass someone (which happens to people of all identities and points of view on gender and I would want that made clear if it's going to be approach) is different so I'd want to know how that was covered. That would concern me far more than gender neutral language in the context given.
I think in the current situation the schools really are doing their best to "be kind" (and in this situation this is an appropriate way to describe it) to teens just starting to navigate their personal and sexual identities, in the middle of a pandemic and school closures.
I do think it is in large part the schools generally wanting to "be kind" and there is a lot of pressure for them to find a balance with very limited support and conflicting messages of what they're meant to do.
Even before all the COVID issues that have just compounded things, puberty is a difficult time and there are so many messages around identity that schools are trying to figure things out while things keep quickly changing that I imagine it's hard for many staff in schools trying to figure out how to handle these things.
I don't think it's helped that sexual identities have often been mixed into gender identities.
It was interesting when touring a new build school recently that when it was discussed that there were girl, boys, and unisex toilets in a particular area, one person nodded and said very confidently "for trans students". The headteacher giving the tour clarified that they were for anyone who might prefer them and, in this area, for guests into the building. Later, she went on to discuss that their main focus in giving students time to figure things out, not to put them into a box so no, the unisex toilets are not to be labelled as for trans students. They are simply the unisex toilets or the gender neutral toilets.
It was actually a thing for the school that some of the students had thought all the toilets in the new build would be unisex. It upset a lot of them and it had to be retold to everyone that wasn't the case.
And if you're going to start with the "genitals = someones gender identity" then I'm sorry but, you are 100% transphobic.
Also, stop being so obsessed with people's genitals, it's weird.
Someone's sex is far far more than their genitals. There are many dysphoric who actually have more distress around our other sex traits that are visible (or audible, voice is a huge thing for many), because part of it is how we are perceived by others. Erasing our sex down to our genitals is to erase how gender dysphoria works and doing it to mock and dismiss those who prioritize sex over gender identity doesn't change that.
Male and female aren't gender identities, it's how we sex everything including plants and yes, even dysphoric people are male or female. How we want to be seen can differ from that, but as treating gender dysphoria has changed with the times and will continue to do so, the whole 'doesn't fit neatly' as a model for gender issues isn't a universally recognized one and some find it harmful, it treats us as having failed at our sex for having issues with it and being percieved as it.
I don't have the hubris to think I have any fucking idea what future generations will think, but what I wish is that one day, as a society, we will realize the risks of individualism and having practically everything as commodity to be sold to us including gender these days is that our sense of self is treated as both innate and as a preference, which means our way of being are treated as consumables.
It is in part a backlash to more rigid models, but as one of many models for identity, I think the pendulum is being swung too far and the results won't be as inclusive or 'our true selves' as some like to think anymore than other radical identity shifts.
Classic example of privileged people mistaking a slight inconvenience as some form of opression.
Might want to look into research on teaching people about privilege. All I've read so far is that it doesn't make those in power nicer, it just makes them meaner to their own without considering wider context -- so White people taught privilege tend to be crueler to other White people regardless of any intersections, but it makes them no nicer to marginalized ethnicities. Not sure what it is about the ape brain that makes us think just making it harder for each other is enough, but it's been shown time and again it doesn't help anyone. It's useful in theory and discussions around the topic, but it's failed in practice for improving how people treat others.
Happy for gender to be erased. Prefer my 2 sons and 2 daughters to just be treated as people and not as boys or girls.
For me, it depends on the context and I think it does for them too.
A talk as described, I likely wouldn't notice much.
When my son was little and dealt with a lot of shite over wearing his hair long and with headbands (to meet the same rules as the girls), he definitely wanted his sex recognized. He sobbed about how he just wanted to be seen as a 'cool dude'.
When my he was being sexual harassed at 15, I wanted his and the adult perpetrators sex and ages recognized.
When my daughter was a victim of peer-on-peer abuse, I wanted it recognize that it was boy-on-girl abuse, it was specifically about her being female and he thought girls should do that was being targeted.
When after that she and her siblings joined a local protest about violence against girls and women in our community, and I had some stranger come up to me to tell me how she thought it disgusting that I let my kids participate and even after explaining I was supporting my daughter's choice, I got told 'don't you know men get raped too?, I really wish that person could have recognized that while that is true, what my daughter really wanted at that time was to seen as a girl safely and be supported. She needed what was used against her to be valued and protected.
While there are risks to focusing too much of our sense of self on demographics, there are benefits to focusing on them a bit for a time and in having them recognized and seen as important by others when relevant.