I think crashing can easily hurt the confidence of an athlete. It can lead to anxiety in similar situations. It can also lead the athlete to take fewer chances in situations that might require a more aggressive approach.
One way cyclists can overcome the fear of crashing is through exposure therapy. One type of “exposure” can involve the cyclist imagining situations similar to the crash. The cyclist can imagine the sights, sounds, physical sensations, and thoughts related to the situation.
It would also probably be helpful if the cyclist had a game plan for what to do in the case of a crash. Practicing the game plan in training would likely be very helpful.