My understanding was that the human race would not be where it is today without the development towards eating meat.
Humanity started as herbivores, as are most modern primates, but during the Pleistocene era, there was a massive worldwide drought, climatic change, and forests, for the most part, died out. Humans, as they existed then, started to scavenge for food to survive, and that meant including meat in their diet, although they were not yet able to kill their own animals. Their digestive tracts changed over many generations, as did their brain size and intelligence. Eventually they transitioned from scavenger to hunter when we discovered the use of bones as tools and weapons. Agriculture followed, animals were domesticated to make farming easier, and civilisations grew from there.
That is a very broad generalisation of the theory, so please don't nit pick on the details. But as I understand it, if we had stayed vegetarian, humans would be extinct by now, or at the very least, certainly not the dominant species on the planet.
I also remember reading somewhere that being carnivorous or omivorous is directly relatable to brain size, that human brains grew because we started eating meat (not for a second am I suggesting that vegetarians are stupider than meat eaters, I'm talking about a long term change in human physiology).
I'm not suggesting that vegetarianism is wrong, I just disagree with the sentiment that humans were never "designed" to eat meat. For starters, that suggests that we were "designed" by someone, not simply a product of genetic selection over time to promote survival features (sorry, I believe in evolution, not creationism). Secondly, current theories do suggest that we have benefitted from meat eating.
By the same token, I don't believe we were "designed" to eat meat either. I just think that's the way our species has evolved. Obviously our bodies can handle meat because the majority of the population does it every day. It can cause health problems, but so can many, many other things that the human body ingests, such as alcohol and fat.