It is in the nature of phobias that they are irrational but hearing people tell me that it’s silly to be scared of spiders does get a bit annoying, so instead of telling them I can’t help it I decided to do a bit of reading so I can give a more scientific response.
One of the best tools for investigating how the brain works is functional magnetic resonance imaging (fMRI). This is a fancy name for a brain scan that takes pictures of your brain while it's doing something. The advantage is that instead of just getting a picture of how the brain looks you get colours that tell you which bits of the brain are working and which bits are switched off. This has been used to help us understand illnesses such as depression and schizophrenia and also to explore "normal" human behavior for example listening to music and telling lies.
It has been used investigate what is going on when someone like me sees a spider and runs screaming compared to my wife who simply scoops it up and places it gently in the garden. A team at the University of Rome reviewed the research and found that in people with phobias the bits of the of the brain that get switched on in fearful situations were too active. They also found out that the body reacts more strongly than usual to these fear signals. The good news is that they also found out that treatments such as systematic desensitisation change these back to "normal".
So now you know and the next time someone tells you "it’s stupid to be afraid of spiders” you can tell them that it’s not your fault: it is due to “over activation in your dorsolateral prefrontal cortex associated with dysregulation in your limbic system!”
That should keep them quiet for a bit.