Cyclophobia, the fear of bicycles, is more common than you think.
I blame training wheels. These contraptions lure children into thinking they can ride a bike. When the training wheels are removed this false sense of security is destroyed in an often traumatizing experience.
In Europe, where adults use bikes without strong irrational fear, children learn how to balance before pedaling. These "balance bikes" don't create a false sense of security and leave the continent largely free of cyclophobics.
For whatever reason, Americans tend to falsely believe they are much safer behind the wheel than behind the handlebar.