Here's my quick thoughts in the subject.
Clearly to many people, diving is extremely dangerous and were all going to die.
This is what half of my family think. It doesn't matter what I explain to them, sometimes it actually makes it worse (explaining redundancy in some cases). But they all love seeing photos and videos of my excursions
The part that I'm realizing is that we're going out of the atmosphere that we know for the entirety of our lives after we're born. In their mind, we might as well be floating in space. If something goes wrong on land, we're still able to breath, even if we loose consciousness, break a bone, have most medical emergencies.
I could go hiking, spelunking, downhill mountain biking and they wouldn't worry nearly as much as when I go diving.
Even driving my car to work is more dangerous and life threatening!
I think one of the main fears is being out of the breathing atmosphere. If we find a way to convey that it is a safer activity than driving to work, and it's not big, dark, cold and scary as the Bearing Sea is on TV. That you don't have to go deep, in rough weather, and that most sharks and other 'scary' animals are more likely to be scared off by you, then maybe we can then work on conveying the cool and fun factor.
Seeing pretty reef fish, coral, shrimps, octopus, squids, snails, nudibranchs, lobsters, etc. neat wrecks (natural or artificial). The team (buddy) atmosphere. The same hangouts as other sports like skiing. Hanging out after a day of diving over food and beverage, the camaraderie during setup, tear down, SI's.
Sure there are miserable days of diving where the weather sucks, the heater doesn't work on the boat, cold food, leaky dry suits, bad vis, etc. But that's rarely the majority.
BRad