A person can be killed instantly through many different means.
As we know it, to be killed painlessly, is to be killed instantly.
If you instantly destroy a person's entire brain then they died without pain.
Yet the most effective ways of instantly destroying someone's entire brain are considered inhumane.
If instantly killing someone by smashing their head with a massive rock, or shooting them in the brain stem is inhumane, then there is no humane way to kill someone at all.
Self-defense is inhumane? Call out the invader first, please, then we can talk about whether the defender is overdoing it.
Killing is inhumane.
Killing in self defense might be necessary, yet it does not become humane just because you want it to.