Get a mirror and learn how to use it. Learn how to take the lane when necessary. Watch cars coming from behind. You'll learn to detect possible lane wanderers, etc, soon. In 60 years of riding and over 35 of touring, I've left the road many times because of bad drivers coming from behind. I've also left the road because of drivers passing coming at me in my lane. I know a lot riders don't use a mirror. That's their choice, but they are completely at the mercy of drivers from the rear taking them out with no warning.
Anyway, learn to ride safely and get lots of practice. You can tilt the odds in your favor. Although I've been in several bike accidents, and a few with cars (right hooking me both times), I have learned, and it's been years since I've had a problem.
I don't think you can honestly tell her that riding is safe. I've also spent decades rock climbing and mountain climbing and my wife knows all of this is not safe, but also knows that I am experienced and examine the potential dangers and work to minimize risk.
BTW, without these "risky" sports and the adventure and joy they bring, I would not be a happy husband.