I think people look down on kids way too much nowadays. remember, there was a time when 12 year olds were considered adults and part of the work force just like a 20 year old (If memory serves, King Tut. was 12). A 15 year old can steal a car as well as any 30 year old car thief. Kids, especially teens, can potentially be just as capable as anyone else - they just lack physical size. They may or may not lack experience - is a 14 year old with 300 logged dives going to be less help than a newly certified diver with only the mandatatory 4 OW dives under their belt?
I think it's more a case of the parents, having brought their child into the world, and still rememebering the changing of nappies, feeding at 2am and the general helplessness of their child as a baby, still seeing this in their teens. I'm 31 and my dad still treats me like a 3 year old at times. Heck, on a recent trip to Europe, my 60 year old Auntie wanted to escort me and m 20-ish year old cousins to Budapest to keep us safe from any "bad people".
The only potential danger with a child is a short attention spand, but, from my memories of being a kid, or a teen, if I was doing something I loved (I'm guessing diving would qualify for most kids and teens) my attention would be 100% there - for as many hours as the activity went on.
Whilst yes, it is your precious child you are diving with, and I, too, would take all the precautions I could to keep them safe, don't underestimate what they can do in the case of an mergency. With the right training, they can be capable of doing what is needed to make the difference.
Z...