I'm with my friend Ed, it would 'depend' on maturity. If they are mature enough to take it responsibly, and take care of the razor and other equipment and not make it a 'show and tell' thing then I would encourage it (with parental consent).
In the days gone by that was the only way that a young man would be shaving. They would have learned from a father, older brother, uncle and or even a neighbor.
At 13 he would be a year younger than our parkerskouson who as best as I know is the youngest member at joining time here at the ripe old age of 14.
http://straightrazorpalace.com/membe...erskouson.html
For some reason, his video of his first shave doesn't seem to exit anymore, I'll get in touch with my young friend and see if he can re post it here and perhaps even share his thoughts about all of this/maybe even his folks thoughts :shrug: