Before my kids were born I was involved in what many people would describe as dangerous sports - street riding, rock climbing, mountaineering, etc. Once they were born we naturally included them in those activities. As a father, I always sought to expose my children to potentially dangerous activities in safe ways. It was important to me that they grew up with a healthy fear of what could happen when things go wrong. And know how to use equipment and safety devices to do dangerous things safely.
I've taught my kids about gun safety & shooting, sea kayaking, riding, technical climbing, mountaineering, etc. We started when they were young enough to listen and obey. We continued as long as they showed interest. I believe my children (now all 25-30) are safer because they learned about these potentially dangerous activities in a safe way, fully cognizant of the dire nature of the hazards and aware of the techniques and tools available to eliminate or at least mitigate the hazards.
That being said, I would not push anyone towards any dangerous activity, riding included. I've been riding since I was 16 (now 58) and barely survived my early years on a street bike. I don't regret the experience, but I wouldn't want my children taking those risks. I wouldn't stop them, but I'd use all my influence to educate them and teach them to avoid the hazards and survive the inevitable crashes.
Now that I'm a new grandfather, I have to consider how I will handle these issues with my grandson, when and if he shows interest in these things. It's a tough call either way.