“Ok Nerr so if you had, say, a 16 year old with anorexia who wanted to refuse treatment and basically starve herself to death, you'd give her your blessing would you? Or a child with schizophrenia who wanted to come off meds against doctor's advice?”
This ^^. I would also ask this of QueenAravisOfArchenland
I assume that those saying the OP IBU don’t have teenagers with mental health problems. Don’t judge until you have walked in those shoes 
Spot on RagingFemininist
“I would be surprised if many 16 year olds would let their parents make or attend their medical appointments”
Really? DD wouldn’t go on her own, even if she could. I have just asked her and she says she would prefer me to go with her. But then she has anxiety – and is undergoing treatment for it. Clearly most parents on this thread have teenagers who don’t suffer from anxiety/depression/self-confidence issues. I would ask you not to judge parents of teenagers who do.
“When dd got to 16, I stopped attending with her - I’d be in the waiting room, but not in the consultation. She’d come out and we’d go home together”
That’s what we do Jux, although DD sometimes wants me to come in with her to start with to outline what the issue is as she sometimes clams up and can’t say anything.