Like most things in life, it's exactly as dangerous as you make it.
As Terry points out diving is much like other sports that we choose to be a part of. Be it biking, sailing, ATV's, hockey, etc. There is always an element of risk but manageable with training and preparation under normal conditions. There are always conditions that no matter how much training and prep you do, whatever sport people get hurt. Yes people die riding bikes, sailing, riding ATV's, etc. there you have it. As sports go I think it is safer than most if you run the numbers. But that is going on hear say / conjecture on my part. I have not currently reviewed the statistics.
To put your relatives at ease, share the OW manuel with them or show them the DVD.
Help them to understand that recreational diving is very quite safe when you adhere to safe diving principals. This will work for 90% of them but your mother will never see it that way! Mine still refuses to talk about it.
I am about to start OW training with my youngest 11 year old, which will make the whole family divers. I do not know any other sport that I would rather pass on to my kids. A life long healthy activity that they can take with them. Diving teaches us to be responsible and not complacent for we all should live life ignorance free! Just my opinion there.
Have fun and be safe diving, play by the rules!
CamG Keep diving....keep training....keep learning!