If it's okay for people to do that, why isn't it okay for the home owner to do this then?

If a person's neighbors keep letting their cats outside to roam and their cats keep coming onto a home owner's property and killing widlife that they worked to build a habitat for, and the cats keep digging in their gardens, leaving feces on their walkway, coming up to the windows and driving their dog crazy, and otherwise being a nuisance and trespassing, then why wouldn't it be okay for the home owner to let their dog (who hates cats) outside when they see trespassing cats if the dog never leaves the home owner's property?