A pet cat is privately owned property of someone, so you are destroying their property.
While feral cats may seem like a pest, they really don’t live off garbage. They live off rodents. Rodents are quite bad. Some have said a major factor in the introduction of the Bubonic plague (Black Death) in parts of Europe was a wave of “cat killing” (the Christians decided they were really witches).
Killing some insects may raise a similar problem. For example, most spiders are harmless to humans, they eat meany mean and nasty (from a human perspective) insects.
Then of course, there is the halachic issue of causing unnecessary pain to animals, which would apply even to animals that are annoying or dangerous to humans, and all the more so to those that are beneficials (such as ones that kill rats, or mosquitoes).