The answer can be found from evolutionary psychology.

> Evolutionary psychologists argue that much of human behavior is the   
> output of psychological adaptations that evolved to solve recurrent   
> problems in human ancestral environments

Spiders and snakes were major threads in the early years of the evolutionary history of humans. Human ancestors that were more afraid of spiders/snakes had an evolutionary advantage over those who did not, because they were more cautious and survived more years.

> people nonetheless learn to fear spiders and snakes about as easily as
> they do a pointed gun, and more easily than an unpointed gun, rabbits
> or flowers. A potential explanation is that spiders and snakes
> were a threat to human ancestors throughout the Pleistocene, whereas
> guns (and rabbits and flowers) were not. There is thus a mismatch
> between humans' evolved fear-learning psychology and the modern
> environment.