Being an omnivore doesn't mean that you have to eat meat in order to survive, it just means that you can eat meat. A vegetarian is still an omnivore also because they eat milk, eggs, and cheese, which are all animal products that would preclude them from being considered in any of the traditional classifications (frugivore, insectivore, herbivore, etc). At the same time, we do not really have significantly carnivorous teeth. We most closely resemble frugivores in our teeth pattern.
Notice how significantly pronounced the carnivore's incisors are. Those were evolved for a clear purpose, sheering and biting into their prey, as both a weapon and an implement for tearing up their prey. Notice also how sharp their molars are, for further sheering before digestion.
Now look at a human's incisors. Still have some pronouncement, but definitely not that much compared to the carnivore. They are more significant than the frugivore's however, which is not surprising since meat has certainly been an ancillary part of our diet and some of our primate cousins' diets (like Chimpanzees, the earlier humans, neanderthals, etc).
Also notice the similarity in the molars, how they are relatively flat and relatively the same size as the rest of our teeth. The closest to us are obviously the frugivores. If you think about eating a fruit, it's very obvious why that would be the case. Furthermore it makes sense that humans would eat a lot of fruit, since that would be the easiest source of food to find and eat. A lot of the vegetables and starches that we now eat are relatively recent in their domestication, whereas fruits are a relatively safe bet and can be reliably determined to not be poisonous.
Humans have sought meat as part necessity and part status symbol, really. At this point the problem with advocating immediate ending of all meat consumption is that all of our agricultural systems are set up to profit, and meat is a huge profit once you consider all the subsidies. I think the best course of action is to take away the subsidies on meat and create much higher standards of animal treatment as well as enforcement of our current cruelty laws.
Personally I think eating meat is bad for you and the environment. I understand the strong cultural attachment to meat, but don't think it's right to take the life of an animal that doesn't want to die. Regardless of what we can eat, and what other animals eat, that doesn't mean it's right for us to personally kill other animals since we know better.
Even accepting that it's ok to kill other animals, I still think it's wrong for us to have slaughterhouses and to treat animals like an object rather than a form of life that can suffer/feel pain, have families that they love and care for, and have unique individual personalities. Anyone that has ever raised animals know that all those things are true. So why do we treat animals like they are commercial products? Because if we acknowledged an animal's right to life we would have to question our own lifestyle up to this point and how we have benefited from the exploitation of animals. It's much simpler to say that animals have no rights than it is to come to grips with how much suffering we have been responsible for in order for us to enjoy our dinners more.
The big problem is that eating animals is way too resource intensive. Why? Simple ecology. The most efficient form of energy production in the animal kingdom is photosynthesis. It is the only way that energy is introduced into ecological systems. Right above that are the herbivores/primary consumers, but they have to eat the plants/primary producers in order to get their energy, and a large amount of that energy is used as they grow and generally go about their day to day lives (moving, standing, even resting uses energy). So even the fattest cow that has the most meat on its bones is always going to have use a large amount of resources that will never be passed on. If we want to feed everyone the most efficiently, we would go directly to the source of energy, which is the plants.
Our refusal to do so is killing us, both environment and health wise. We'll see what happens in time, though.