To the truly uninformed, I always get the "OMG, SHARKS!! YOUZE GONNA BEE EATEN!!" From the slightly less uninformed, I do explain some of the dangers of diving (mostly because they already know it's dangerous) but I make sure I inform them that, while it's dangerous, nearly all of the risk is mitigated by proper training. And then I lie and tell them that the training in their certification courses is more than enough to keep them safe, as long as they practice. I also use some funny statistic to back up the safety of recreational diving.
To the more informed, and to those that have some technical yearning, I do explain some of the technical aspects of diving. I mention Oxygen Toxicity (as a way to bring up "air" vs "oxygen" bottles) and Narcosis (to bring up Trimix diving). I talk about soft vs hard overheads, and how all of your training is specifically how to get yourself out of any situation alive, even if alone. I mention that cave training is done (another lie) only by the most experienced and respected divers, and that (this is the truth again) that I'm fully confident that my instructors could get me to where I needed to be in terms of physical and mental preparation for any situation. If someone still seems to be frightened, I make an extra point to talk about how only the extreme few get into truly technical diving...but that for those that do, the rewards is truly worth the effort and the risk. The beauty and the serenity at those locations that so few have been to is worth every second of arduous effort to get there. I also explain how strict my instructor was on safety drills. I explain how I swam out 1300' with no lights and no visibility, from way back in a cave, with a buddy, when one of us "randomly" ran out of gas (because of the instructor) and how we had to make navigational decisions in that visibility and in those conditions. I explain to them what my instructors told me: The only two things you need in a cave are: 1) breathable gas, 2) continuous guideline. I then explain the redundant air supply, "thirds", and lost line drills. I explain that the only thing that could possibly keep me in a cave forever was a mental mistake, and that as long as I was focused and aware that I would always be fine. All of that is wrapped up with a: "But that is only for REALLY experienced divers that have TONS of time and training. Recreational diving is incredibly safe when done right, and very safe even when done fairly wrong.