So if you are serious about learning to fly you are better off paying money and working with a dedicated flying traing organisation, rather than a cheap, aviation-themed youth club? You don't say!
If you have the brains and the limb-length to operate the aircraft correctly you can fly the aircraft.
However, taking that solo requires an understanding of personal responsibility to obey the rules of the air and to operate the aircraft in accordance with your training and the operator's manual - it is not a car that you can thrash around the back roads or do doughnuts with in a supermarket car park.
The flip-side is that flying an aircraft solo does not benefit particularly from life experience; only time flying is of any real benefit. To me, 14 does sound a little young this is based on the psychology of responsibility and not any concept of wisdom, but where would you set the bar? You drive at 17 in the UK but the psychology is still there, so would it need to be older?
Maybe the experience of flying is sufficiently different that 14 is a reasonable bar. I wonder if there is a higher age limit for taking a passenger.