Children can't vote but their parents can and their base fear government telling them how to raise their children. This strategy forces liberals into a no win situation were they will always look like their goal is to brainwash their kids. That fear is something a lot of fence sitters already fear.
It is a type of reasoning, just a bit twisted. By giving kids the ability to transition or seek medical interventions, you're also taking away the parents ability to control their kids, forced by the state which is a quick jump on the conclusions map to the other belief they've set up previously which is the state is brain washing kids to become trans through the state run education system.
So in their view, the liberals are forcing trans ideology on children while trying to remove parental rights.
No. Responsibility is not ownership. You have an obligation to your kids, not the other way around. If the kid doesn't want to tell you a profound secret about who they are, then it's time to reflect on your parenting, not to get the government to force teachers to rat them out.