1. The idea that you can only find sufficient protein in meat is propaganda, courtesy of the meat industry. Read about the China Study for more on that, and on dairy.
2. The world would be overrun? What, chickens are going to organize and march on our capitols? Explain to me exactly what you mean by that.
3. "If they can do it, why not us?" They eat meat to survive. We eat meat because we like it, not because we need it. Humans are extremely overpopulated thanks to medicine and other lifespan-increasing advances. If we want to stay overpopulated, we need to consume less.