I can see what people are worried about. Children are notorious for going throuhg 'phases', imitating their friends, etc. People 'try on' a lot of personae before they find out who they 'really' are.

There is a very real fear among people that to initiate gender reassignments and related therapy before the patient is an adult able to make an informed decision for themselves is somehow medically dangerous and morally wrong.

This doesn't, in and of itself, come from any kind of phobia or prejudice. Just a general and near-universal urge to 'protect' children. As such, it's going to be really, really hard to overcome.