Children depend on various adults to make good choices for them. You can't just let people do "their own stuff" to people in their care.

There is a legitimate medical concern that it is difficult to differentiate between a tween experiencing gender dysphoria and a tween who is anxious about their body/mind changing against their will during puberty.

A kid lives the first dozen or so years of their life being largely agendered and asexualized. The prospect of suddenly being sexualized and having gendered perceptions and expectations thrust upon them without choice is scary. Especially for girls, who start dealing with sexual harassment around 12, getting their period and think... man this kinda sucks, I miss when grown men didn't creep on me and I wasn't bleeding 1/4 of the time. Most tweens would avoid puberty if you gave them the option.

I don't think informed consent should be the standard for minors getting puberty blockers, and psychologists need to certify that the kids aren't experiencing anxiety/dysphoria over puberty.

I will have to dig up some of the research I read on this, but it aligned with my personal observations dealing with kids.