"after including an animal most cultures typically view as a companion instead of a threat." Though if it is cruel to hunt a cat, it is cruel to hunt an animal that is a threat. The concern in these cases seems to be less about the animals and more about the feelings of the humans (which are of course relevant, but we should be clear about what the real issue is).
It is also less cruel to humanely dispatch a caged animal than to shoot a free roaming one (which has a fairly high likelihood of simply being wounded and suffering before dying). Anyway, it isn't considered cruel to trap a cat in an box trap, as when capturing to take to a rescue (keep in mind that feral cats do not get rehomed) or when trapping for TNR programs (which is another can of worms).