Well, we think that murder is wrong, and that it's often (usually?) not just wrong but very wrong—wrong enough to count as evil. Robbing someone of their purse is bad; robbing them of the life is worse. What you say you don't understand is why we count murder as (typically? often? almost always?) evil in spite of the fact that we think killing isn't always wrong. You see some sort of hypocrisy here. But why?
After all: not all killing is wrong. The obvious example: killing in self-defense, which I hope we can agree is morally acceptable in a way that murder isn't. Even more so: killing by a police officer to protect the life of an innocent person threatened by an assailant. Capital punishment is a harder case. I think it's wrong, but I don't think people who believe otherwise are therefore morally blind. War is complicated business, but there's a case to be made that going to war is at least sometimes morally acceptable too.
The place where what you're saying seems to miss the mark is here:
it seems hypocritical to me that we as a society generalize the idea of killing as evil when relatively many of us favor capital punishment, strong military, and, at least in fiction, vigilante justice.
and it misses the mark because to think that some but not all killing is wrong is exactly not to generalize the idea of killing as "evil." It's to make distinctions. That's consistent with a rule of thumb that says killing is presumptively wrong and always needs justification. But it seems clear that some killing in some circumstances can be justified. That's true even if killing is usually wrong. It's true even if most (but not all) killing is positively evil.
I'd add one more thing: talking about "we as a society" is usually not helpful. "Society" isn't one thing. Different people within a single society hold different views, and hold them with different levels of conviction. Rather than worrying about what "we as a society" think or say, better to analyze the views themselves. And the word "hypocritical" applies to societies, if at all, only as a not-very-helpful extension of its primary use: as a way of describing individual people who are guilty of a certain sort of moral weaselry.