For years I wouldn't accept people under 18 until one of my students, who ran his own dojo, surprised me by turning up to a grading with a bunch of 15 and 16 year olds. What I saw in terms of quality technique and the sense of fun and excitement they brought with them convinced me to change. (My wife, a state judo champion at age 14, had been suggesting this for years!)

Once I got used to students answering 'cool' when their technique was corrected, turning somersaults when only a backward roll was required, or being asked to teach 'ninja' techniques, life in the dojo became more fun, more interesting and more fulfilling- for everyone. I graded the first of this new generation to Shodan when he reached 19 and have to say that technically he was one of the best shodans ever. He's still training, (at another dojo), and is, I hear, a very strong Nidan.

It opened my head to possibilities and stopped me becoming an old grouch- well almost! I haven't much to add to the excellent comments by other posters except to say in my experience teenagers love to train (and talk) hard.