There has not been a single vegetarian civilization to make it into the history books. All people, from the dawn of humanity, have eaten meat and indeed the eating of meat is what made our species what it is today.
In our modern times, with our modern approach to food, yes it is possible for some people to live on vegetables and other non-meat products. When vegetables, nuts and other nutrients are flown in by plane from around the world a vegetarian or vegan might eat well indeed.
Humanity will give up eating meat when we have advanced to the point where our nutrient source becomes utterly irrelevant. That's not going to happen any time soon. Our technology right now allows for vegetarians to experiment with this new lifestyle but it is not something any sane leader would impose on their people.
For context, vegetarians would do well to place their lifestyle in our history. It is unreasonable and unprecidented to shame people into a non-meat diet. It is radically new territory and not at all apart of the human condition.