And one is accepted, understood, and valued as biological scientific fact.
The other is based on theories that relate nothing to science.
Gender is based on theories that relate nothing to science? Rejecting the idea of gender as distinct from sex is a pretty ridiculous idea considering it's an ironclad fact. There are (effectively) only two biological sexes and there are numerous examples of societies with more than two socially recognized gender roles. If there are only two sexes and more than two genders, gender is obviously distinct from sex. If you don't like that this is the case that's fine but you can't expect us to indulge you in the idea that it doesn't exist.
One is to be respected and acknowledged as fact, the other is "it makes me feel good" and is often prone to abuse.
Asking for someone to call you by your preferred pronoun is literally the smallest thing I can think of to ask of another person. More importantly, they were ordered to do so by their boss.
This teacher has a lot of growing up to do because he seems to think he has some sort of inherent right to ignore his boss and refer to students however he wants to. He doesn't.
IMO pronoun changes and requiring me to utilize them whenever addressing you aren't acceptable. Name changes are acceptable. You can't control your biology in life, but you can control your name... especially if your parents gave you a crappy one or something.
That's your choice to make! It's also your boss's choice to make to fire you over it if you refuse to abide by your workplace's code of conduct.
I'm not sure why you keep mentioning biology though because gender is not biological in origin, it's cultural in origin.