This isn't really about humans killing each other- it's more of a self-preservation instinct that helped mankind survive and eventually evolve through time. That instinct kicks in when we feel threatened by anything at all, be that the person in front of us, the news that people talk about us behind our backs, or the mere "defensive stance" when someone defends himself against accusations.
The preservation instinct is not to kill, but to neutralize a threat. The "neutralization" methods will vary from one mindset to another.
but you have to agree violence is the first thing we think of. If someone is in our way, we want to shove them. If someone is talking shit behind your back, you want to hit them. Even if people don't act on it, they think about it. The fact that it crosses their mind says a lot about how violence seems to be a part of us.
So it's not just about a killer instinct, but a violent one.
I'd like to think that everyone has at least felt violent towards someone. Most that do feel that way, never talk about it openly because of the fear of being called a psycho.
From what I am aware, humans developed organized warfare as a way to gain resources and extra mates. Apparently humans and chimpanzees are the only species that developed warfare as an adaptation. As far as animals killing others of their own species over a mate or territory, that is pretty universal across all animals I think? if the competitor doesn't back down when they should, they will go to the death after all.
So to answer your question, yes, people may resort to killing others in a survival situation.
It's completely natural for a person to have an instinct for self-preservation. If that means putting a permanent end to someone/something that is trying to kill you, then yes, people have an instinct to kill. Going off and actively hunting/killing other people, however, doesn't fall into that self-preservation instinct... unless you come from a cannabalistic society that sees other humans as legit food.