Small planes are certainly not safer than driving. I'm a private pilot and i've studied it at length (and I love flying).
I don't have time to braindump my research, as it's slightly hard to compare fatalities per passenger mile in autos vs per flight hour with light non-commercial aviation. It's about 100,000 hours per 1.9 fatalities which includes commercial travel. It's SIGNIFICANTLY higher in small planes.
The way I summarize it to people in casual conversation is: Flying a Cessna is safer than riding a motorcycle but more dangerous than driving a car.