I've just listened to the recording again.
I don't think it is clear whether the child who claims to identify as a cat is actually present or not.
But on the assumption that they are talking about a particular individual, that makes the teacher's response even more dreadful.
If you listen to the end of the recording, the student says, "All I said was, how can you identify as a cat when you're clearly a girl."
Even if they are talking to an individual, that is a fair question.
If the girl who thinks she is a cat was present and was upset, the teacher should have dealt with the situation by saying something like, "Everyone has different beliefs about their identity. Some people believe they identify as the sex they were born as. Some people believe they identify as the opposite sex to the one they were born with. Some people believe they identify as neither male nor female and some people believe they identify as something other than human. Some people don't believe in gender or believe they identify as anything at all. This can be a sensitive topic for discussion and it's absolutely fine to discuss ideas in this classroom, and to state our opinions in a respectful way. But it is not OK to personally attack others who have a different identity or a different opinion, and so I would like you to apologise to Fluffy before we move on with the discussion."
Instead the teacher launched into a polemic where they audibly lost control of the class and branded two teenagers despicable for saying that a girl cannot be a cat.
And as a PP said, if a child believes they identify as a cat, the appropriate response to that, concurrently with dealing with any bullying from other children, is to initiate some sort of mental health checkup. Not to tell the child that their identity is valid and agree to use miaow pronouns from now on. Because that child is going to grow up, and they are going to have to live in the real world, and they are going to have to get some sort of a job if they want a roof over their head and food to eat, and in that world, it is not ever going to be OK to be a cat.
If this nonsense isn't nipped in the bud, Fluffy's parents are going to find themselves still responsible for feeding, clothing and housing their 40 year old, socially outcast, unemployable catchild, and wondering what the hell happens when they die or get too old to parent anymore, but their child isn't recognised as having a genuine disability which would mean social services had a duty of care towards them.
Either that or it's an attention seeking fad which they grow out of within six months, making it even more absurd to try and force other students to respect it, but because the supposed adults let it go on for so long the child will have no friends and will never shake off their reputation for being the crazy nutter who identified as a cat for a while.