I am always surprised by the way car versus plane safety come up. I know how to drive a car, and have control over the situation when I do. This doesn't mean its completely safe, but I can help control the risks. In a plane (or train, or taxi or any mode of transport where I am a passenger) I have almost no control and I expect the transport provider to provide me with transport that is safe. Very safe.
Of course in many cases, car drivers feel like they have much more control over things than they actually do.
Being in a commercial airliner on the other hand, actually emphasizes the feeling of helplessness: you're strapped in a seat and have little room to move, you cannot effect what's happening, you can't even see who's in control, or often even see your surroundings... it's like being trapped in a box tumbling down the mountainside.
I've found that even just unstrapping my seatbelt and taking a quick walk down the aisle on an airplane actually makes me feel safer, even though of course the reverse is actually true. This makes some sense given that human instincts probably value having the ability to flee or react in a dangerous situation but those instincts still exist even in situations where they make no sense.
Thus the perception many people have that they're "safer" in a car than on an airliner, even though the reality is that the odds are very much reversed. Large disparities between perception and reality can of course lead to people making very poor choices...