People often say that airplanes are the safest way to travel.
I have also read that per unit of distance, walking drunk is 8 times more dangerous than driving drunk. (Of course, the real comparison here should be walking drunk vs walking sober.)
An important factor is missing:
The average drunk walking speed is 2 mph. Let's say that the average drunk driving speed is 32 mph.
So, per minute, you go 16 times farther driving, and it's 1/8 as dangerous per mile. So per minute, it's twice as dangerous.
A similar calculation holds for flying. Although per mile planes may be 1/10th as dangerous as cars, they go 10 times faster. So a minute in a car is about as plane as a minute in a car. So if anxiety is proportional to actual danger per second, it is not so crazy to be anxious in an airplane - at least up to the level you feel in cars.