Flying or driving, like anything else, is as safe or as risky as you want to make it. If you choose to drive on a rainy night when you're drunk and then speed, then it's pretty risky.
It's the same with flying, if you don't preflight the plane, try and push through bad weather, or fly reckless or careless, then flying is risky too.
Explain all the steps you've taken to make sure this flight will be safe and comfortable for them. Explain that planes do not just crash for no reason, wings do not fall off, they do not go out of control. Someone pushed the limits of their skills with weather or their mastery of the plane itself. You have to counteract all the years of sensationalistic, inaccurate reporting and BS they've been hearing on TV.
Pick the perfect day for flying and schedule a short flight, and let them know if for any reason they want to call it quits, you will land promptly. This is no time for showing off, because you will definitely make an enemy of aviation for life. Explain what you're doing during the preflight and run up, let them follow along with a sectional if they want, but don't let them have their head down too long, or they'll get airsick. Make all of your turns shallow and gentle, the same with power changes, and let them know in advance what you're doing so they're not surprised.
Remember, people fear what they don't understand.