If some kid is going around dressing differently and telling people to call them by different names and pronouns, then forget the teachers, the students are going to say something to their parents and it will eventually get back to the parents anyway. And then you're going to have parents that are upset the school knew something and didn't bother to inform the parents.
Even if you are a parent that supports troons, you will be upset that adults you trust to watch and teach your children are suddenly keeping certain information from you. It makes you wonder: If the school kept this significant information from me, what else could they be hiding from me? Parents that cannot trust their schools is a recipe for disaster, for both students AND teachers.
Teachers should always inform parents whenever a student is acting different. This has nothing to do with being anti troon. If your kid is acting out (like getting upset more than usual, crying all the time, etc) then we expect teachers to inform the parents. Suddenly trooning out is the same. Maybe the kid is "trans", maybe there's something else going on (Like being abused). Teachers don't know everything. Erin is trying to demonize parent's right to be informed of their child's behavior and wellbeing, and in turn deprive parents from their right to make decisions for their children's wellbeing.
There's also the issue if shit goes south with the kid (such as attempting suicide) and the parents later find out they were identifying as transgender at school, the parents will (rightfully) blame the school. Even if the teachers didn't do anything to encourage it, since they kept it a secret, it looks horrible and you can't fault parents for thinking the school lied because they were doing something wrong that lead to their kid trying to off themselves.
Erin doesn't want to think about how this mindset harms trust between parents and schools, nor the legal nightmare it puts on schools to follow through with it. Nope, he just wants to cope and seethe, and call teachers Nazis. God, you're a terrible father, Erin.
edit: clarity