The teacher could have discussed that telling the cat girl to her face she was mentally not well was inappropriate without going on a personal crusade and rant.
I'm reasonably sure from a second listen that that's not what happened, anyway. A rough transcript of the first few seconds goes something like:
Teacher: How dare you? You just really upset someone, saying things like 'should be in an asylum'.
Pupil: I didn't say that! [Other pupil, simultaneously: …didn't say that!] I just said if they want to identify as a cat or something, then they're, like, genuinely unwell.
Other pupil: And they've gone mentally…
Pupil: Crazy.
Teacher: You were questioning their identity.
Pupil: I wasn't, a question, I was just saying about the genders, I didn't say anything about them.
That sounds to me like there was probably a discussion with another student about identifying as alternative genders, and the girl in the recording brought up cat gender as an absurd example which most people would consider "crazy". The way the girl phrased it, as "I just said if they want to identify as a cat or something", makes it sound like it was her own example, or a reference to an example mentioned earlier, not abuse targeted at an actual catgendered child in the classroom. Otherwise she wouldn't have said "or something".
I guess you could argue that her "I didn't say anything about them" was disingenuous, and by saying that identifying as a cat means you're mentally unwell, she intended to imply that she thought the other student was mentally unwell, which would upset the other student. (Though I thought we were all meant to be accepting of mental health problems these days, so just why it's so offensive for someone to suggest that you may have a mental health problem if you have bizarre beliefs, resulting in distress if you aren't treated or allowed to behave accordingly, is… an interesting one.)
But you could equally say that the example was likely intended to illustrate a general discussion about gender identity, and she really didn't say anything, or intend to imply anything, about the other student. That she was "just saying about the genders" in general, not saying anything about that pupil in particular, and didn't realise the pupil would find it upsetting.
The other pupil might be upset because they inferred that the pupil in the recording was calling them crazy, or because they're not used to having their beliefs about gender challenged and can't tolerate hearing that others don't believe the same as them about gender identity in general. Or the teacher might be completely over-egging the other student's upset, so she can make a point about not sharing opinions others might find challenging. (And given both girls in the recording, without hesitation, jump in to say that the asylum comment is inaccurate, I'm not sure this teacher is reliably reporting what happened.)
Either way, going by what I heard, there was probably no actual catgendered pupil being harangued about their potential insanity.