You are setting that fact. Just like we as a society are setting the punishment for criminals. It's not a law of nature that criminals, or animals, have to die at our hands. That is a choice we make. And if we are already deciding to take the life of a person, talking about "humane" is at best hypocritical.
Capital punishment has been proven to be expensive, cruel, and utterly ineffective at scaring off criminals. So why is it still done, then? There are no logical reasons for it. Yet still people revel in the sense of "justice" stemming from an eye for an eye. It's about revenge, not about keeping victims save or bettering society.
So if cruelty is the point, why worry about how humane it is at all? Someone stabbed their spouse to death? Why not stab them in kind? Hell, I'm sure we can do much better, there's mass murderers and serial killers who have done horrendous things, isn't a humane death to good for them? Why don't we bring back torture? People in the middle ages were quite good at it already, but I'm sure we can do much better by now. Really make them pay for everything they've done.
If you're revolted by that idea, then good. Because that's not how a justice system or a society should function. Revenge is not helping anyone, and should not be the guiding principle in a civilized society.