Your brain is designed to catastrophise things. With early man, the person who decided that the rustling leaves was just the wind, got eaten by a tiger *. If you have a traumatic experience with something, especially at a young age, your brain is going to associate that with catastrophe, and boom, a fear is born.
You can also learn fears from others, ie, I learned my fear of spiders from my mother (also, had some traumatic experiences when I was younger... but already had the fear by that point).
It's not a choice, but it's not random. Fears do pass with experience, though. A common example of this is fear of flying - clocking up enough air miles tends to get people over this (particularly once they have enough for a free upgrade!).
* You can thank Stefan Molyneux for this argument