Wolves and other predators were hunted to near extinction in North America on this rationale. My mother in law kills all spiders and snakes she can on sight.
Guess she doesn't know what snakes eat. Usually if there are snakes around it's because you have rodents. If you're smart you leave the snakes to their business and try to address the rodent problem instead.
Same deal with spiders, they're obligate carnivores. If there are spiders around, that's because there are other bugs about.
Honestly I understand wolf culls a lot more. I don't agree with them, but I understand the rational motive of people who have livestock, pets, or even children.