For those who have a policy of killing spiders on sight, shame on you.
For someone that is highly allergic to many, many types of insects it's more a matter of self preservation. I've been hospitalized once over a damn spider, never again if I can help it...
Search google images for "brown recluse spider bite" and you'll get a better idea of why I feel this way. (Don't do this if you're squeamish though, you've been warned) :P
Most people are allergic to being bitten by a venomous spider to some degree. When I was younger, I was bitten on the eyelid by a spider whilst I was sleeping. I woke up and wasn't able to open my eye. It healed, I was fine after a few days. I don't know which type of spider it was.
I still believe in life. All creatures great and small with the exception of mosquitoes, which is why I'm happy to have spiders living outside the house.
As to being squeamish, I've lived in Australia my whole life and I'm used to 90% of the fauna being poisonous.