Thanks for the elaboration. In my experience with kids they listen to reason and have the capacity for self preservation and avoiding harm, physical and mental. They can understand at their simple level anything that needs to be impressed upon them, no reliance on an authority position is ever needed. I find that transmitting your values to them and giving them freedom to choose after that, does not disappoint.
Letting your kid go trans is not an authority or lack thereof question, it is a matter of transmitting a (sick) value system to them.