Before I met my husband, I was dating a private pilot. On one of our dates, he took me for a ride in his plane, and it was absolutely wonderful. I trusted his ability completely, even though by some people's standards, he wasn't experienced enough. Two weeks after our flight, JFK, Jr. died. He was more experienced than my guy, and that scared me off general aviation for 16 years.
So when my husband expressed interest last year in obtaining his PPL, I was a little nervous. Accidents happen, even to the most conscientious pilots. Every reported accident gets filed into the fear corner of my mind. Unlike car travel, I couldn't use the sheer number of people I knew who survived a plane crash to allay my fears. I refused to go with him for any of his lessons, because it was scary.
It's not that I didn't trust him or his ability, or that I believed some random stranger over him. My fear did not mean that I was unsupportive, either. All the statistics backing the relative safety of GA won't change anyone's mind, just as they didn't change mine. There is a reason that they are called accidents, and while training minimizes the risk, it doesn't eliminate it.
Oddly enough, it took my husband's accident (non-fatal) in January for me to get over my fear. I started lessons in April, and I finally understand how one can reconcile the risk with the sheer thrill.
Hopefully, your wife will come around without you crashing, but understand that fears are not always rational and don't imply a lack of confidence in you. As a formerly fearful wife, I'd just say she loves you and doesn't want to lose you.