Hi G.:
I am an avid snowmobiler, and use to race them as well as sport bikes.
I am a mom of triplets, and would detour my kids from dirt bikes at all costs. Many reasons why, unsafe, hit a bump go over the bars head first, break a jaw or worse a spine.
A friend in California just lost her brother, where at 15 flipped over the bars, of his dirtbike, he was over 6 feet tall. He was paralyzed from the neck down and lived 4 horrible years more after the accident on a dirt bike.
Up the road from me, there is a momorial for a 12 year old that lost his life on a dirt bike.
Sure there are accidents on any motorized vehicles, but the key is being responsible and safe. In the recent Parents magazine there is an article on keeping your kids safe and happy - and one of the leading causes of death is where a parent does not stand his/her ground and just say "no". Its easy to say yes, and see the happy smile, but it is the responsible parent that protects their child.
Whatever you choose to do, I wish you the best!
M.