Maybe they have faced many cases of parents careless or incompetent to raise their children.
Just my 2ct.

I'm a little gray on teenagers as children, but if one does think of it that way (you need a judge's order here for the state to count it the other way) one cannot enter into binding contracts with a child so I wouldn't extend privilege to them.

I get that helping the patient is what doctoring is all about, but a child cannot consent to treatment, and I'm a little uncomfortable giving a doctor a free hand.

It comes to point where parent and child personal abilities involved. Generally children are less experienced in life thus must be ruled by some sort of authority, firstly by parents. In some cases parents shouldn't be parents in first place. I do think marriage ritual should be done by psychiatrist and not the priest to check couple's ability to become a parent.
This would be much easier than giving freedom rights to someone who doesn't know what freedom is and will probably damage the individual. I mean the child in this case. I disagree with gommi on this one.

Again less philosophy, more action. If couples checked for validity to have children then parents would be qualified enough to decide whether they children should have certain freedoms or not. And if not then they would teach their own children how to be qualified for freedom.

Just one point to mention, this is great as teenager to have secrets from you parents but this is what parent care about. When those children will grow up no one will care about their life or their secrets unless they are Britney Spears of some kind.