I feel like it's more that cats as predators can kill many household pests without a lot of backup and also clean up after themselves, while spiders generally have more specific diets with more specialized hunting methods, and instead of cleaning up after themselves, they leave the crushed and drained bodies of their kills wherever they finish their meals.

Also, prehistoric man probably compared the animals in a face-off and said "if I could have one animal as my friend, I'll take the gigantic furry killing machine that takes care of its young instead of the one that I have to chase out of my shoes every morning"