I know that my opinion regarding this topic is not very popular and particularly the certifying agencies will not be happy with it. But anyway - it is my honest opinion, based on my experience of more than 25 years as a diver and more than 20 years as an instructor.
Of course, scuba diving is fun. The agencies tell it to us everyday and most of us experienced a lot of fun themselves while doing it. But nevertheless, we never should forget, that scuba diving means to enter an environment which is potentially hostile to life. We only can survive there by using technical equipment und by adhering to some physical rules. And every mistake we do may end up fatal.
The physical problems for children have been mentioned before in this thread, so I dont want to repeat them.
One big problem with them is that there is simply too little information. And that will remain for a long time, because of course we cant use children as laboratory rabbits to get some database on these effects.
But there are some other points which should be taken into consideration.
One point is, I mentioned it above, that we have to know and to understand some physical laws for to survive underwater. And my experience is that it is very hard for children below the age of 13/14 to understand this physics and physiology stuff really, because it simply is too far beyond what they know from school at that time.
The second important point is that children dont react as rational as adults. They tend to fear much earlier and to fear of things which never would be a problem for an adult. And because of that tendency to fear earlier and faster, they also tend to panic much faster. And this is a really big problem, because we all know, that a diver in panic is trying to reach the surface as fast as possible. And we also know that the shallow waters (down to 10m) are the most dangerous area with regard to a rush to the surface, because in that area the air volume in the lungs will double, if we are not exhaling, and so in that area we have the highest risk for a lung overexpansion injury.
When I started scuba diving in 1984 it was common sense within the agencies, that the minimum age for scuba diving was 14 years. Later on they gave up this common sense and we came to the point where we are today. In the very beginning of this process, I saw this as a great chance as well and I tried teaching children myself. But with time I found out that this was not a good idea and that the agencies promote it just for to get new customers and more certifications. So with time I decided for myself not to accept student divers below somewhere between 13 and 14 years.
Meanwhile I am happy to live in Turkey, because Turkish law prohibits scuba diving with children below the age of 14. And this law prevents me from a lot of discussions.;-)
My recommendation is, if they are really comfortable in the water, have them skin diving and snorkelling until they reach the age of 13/14 years and than they are perfectly prepared for scuba diving.