Just as mirimir said, it is biological norm to draw line between your own kind and everyone else. For example, both dogs and cats don't kill each other, but dog can easily kill a cat.
Yep, cats fight brutally all the time. My wife's old cat was a fighter and had the scars to prove it. No doubt he had killed many cats, and then he eventually succumbed to an infection from a nasty neck wound acquired in a fight.