Truth is, we have pitifully few reources that are self-maintaining as animal stock is. We talk about a 'renewable energy source' as something of the future, but as far as our biology is concerned, nature figured it out billions of years ago. And it's not just meat. Leather, Wool, Milk, Eggs, Silk, Gelotin etc. It's easy when you are in the First World to believe that we can live without these sort of things, but the truth is that for the vast majority of the planet, they are the core elements of survival.
For example, to a Sherpa, a goat is a source of milk, clothing and, eventually, food. They cannot grow Cotton or food crops because they are nomadic and because the climate will not allow it, they would have to fundamentally change their way of life in order to stop using animals. Unless PETA want to actually get into these countries and establish vast textile and hydroponics industries, whether the country involved wishes it or not, they really are just preaching from a position of ignorance.