I don't think there is a reason for him NOT to run it.
1) For those people thinking that he is doing the distance "too early," I would bet that IF he runs in high school he will be much more interested in running whatever his classmates are running (5k cross country, etc). That's how kids work.
2) He's not going to get hurt. It just isn't going to happen. Name a scenario where he gets hurt. If he was hammering 400's at the track 3 days a week, he could get hurt, or burned out, but he isn't, and he won't.
3) Kids that age don't race anything they would think of as "long distance." He's not going to see one dude on the starting line, start talking some smack, and then trade elbows and surges with him for 13.1 miles. He's going to plod along, give high fives to spectators, and stop at the water stations. It's as if people on this board forget what running was like back in middle school...
4) It's good for kids to learn to challenge THEMSELVES. Nobody's pushing him to do it, he's motivated, he has demonstrated the ability and the desire to do it... let him do it! If he was picking up your guitar a couple times a week and trying to figure out out to play, and asked if he could get lessons, I would hope your reaction would be the same- of course!
5) In summary, your son sounds like a motivated kid and the last thing he needs is his dad laying down rules that have no logistical leg to stand on. All the people that are naysayers here are probably running the same half marathon and are worried that he will beat them.