Humans are omnivores, which means we eat whatever is available to us. We do not eat just meat, so we are not carnivores, but neither do we eat just plant matter, so we are not herbivores, either.
This has nothing to do with whether or not we SHOULD kill and eat animals, but only whether or not we actually DO (and obviously we do) and whether or not we are biologically carnivores, herbivores, or omnivores.
Humans can be perfectly healthy as herbivores so long as they plan their diet carefully. When humans eat meat to the exclusion of other foods they will soon become sick, malnourished, and may eventually die. But when humans eat nothing but plant matter, the same thing can (and does) happen.
Quotations in this answer are taken from the Related Question below, by User Nij: "Humans have developed with the ability to eat a hugely varied diet, which can and does include meats of all kinds. It does not have to include meat, but rather, it can when needed and when this is the better option. We cannot rely solely on meat, just as we are not absolutely able to rely on plants alone (i.e. only the plants available in the early human habitat).
In short, humans are omnivores: we eat what we can because it's easier than eating something else. This will sometimes mean eating meat, and hence we are suited to this task as well as any other."
We have incisor teeth for cutting and tearing flesh, and we require small amounts of animal products to live. Humans require the full range of proteins and enzymes that come only from animal products. You really do not need very much of these nutrients (a glass of milk, or a salad with some egg and cheese slices, maybe twice a week, is plenty). But we DO need them.
Vegans (people who eat no animal products, not even eggs or dairy products) have to plan their diets very carefully, to make sure they do not become malnourished from lack of animal products. "They have to mix certain plant products together to make a complete protein, and many of these are not found in the areas where humans evolved from other hominids. Moreover, the human intestine and digestive system cannot digest cellulose - in human dietary listings, normally known as fibre - in large quantities. Cellulose is the major component of many herbivores, yet if we are meant to be like them, why can we not do it too?"
Some vegetarians or vegans try to argue that humans are herbivores, but this simply isn't true. We are omnivores.
Keep in mind that this says absolutely NOTHING at all about whether it's right or wrong to kill animals, or the validity of other vegetarian/vegan beliefs. There is nothing wrong with being a vegetarian or vegan! Becoming a vegetarian/vegan is a religious, philosophical, moral, or spiritual one, and vegetarians/vegans deserve nothing but respect for their beliefs.
But that isn't the issue here. The issue is whether humans are omnivores, and we are. It is a scientific fact.
It is also important to note that not all vegetarians/vegans believe that humans are herbivores. I have known plenty of vegetarians/vegans who freely admit that humans are omnivores. I was one of them myself, actually. I was a vegetarian for over a decade, but not for one second did I ever believe that humans are herbivores. You are not required to believe that humans are herbivores to be a vegetarian or vegan.