I didn't want to spam up that thread but.. animals are bred for slaughter, like you said. So if the entire world stopped eating meat, animals would stop being bred for slaughter, and they wouldn't die out.. There wouldn't be any cows in the wild lol. People would continue to use cows for milk and stuff. The only reason there is an overpopulation of animals is because of the breeding for slaughter bit.
Another thing is, if people stopped eating meat, it'd solve a lot of hunger problems since the grain and stuff needed to feed cows is a hell of a lot more than needed to feed humans. It's pretty much a waste of grain if you ask me.