I completed cavern and intro to cave a couple of months ago.
After I finished the class, my wife read some posts and told me she enjoyed reading about cave diving, but she wished it wasn't me in the cave. She is certified, although she has not dived in years. I have spent a lot of time explaining the safety procedures and caution we take in caves.
Honestly, it didn't make much difference. I think she has a vision of caves being small, clausterphobic and very dangerous.
The best I've been able to do is get her to agree that she knows I am safe and cautious. That's probably the best you are going to get.
Incidentally, those statistics about it being safer to cave dive than, say, drive to the dive site are not actually valid. The stats would only apply if everyone driving at that time and place were headed to the dive site or if you only included people driving to the dive site.
It is, however, very safe to say that a properly trained cavern or cave diver is very unlikely to suffer a mishap if he or she follows their training. It is also probably reasonable to say that cavern training will make you a better and safer diver overall, thereby reducing your chance of an accident or incident in all your diving.
Good luck.
Jeff