I think you phrased your argument quite well. It's insane to demand that everyone become a vegetarian. I think Americans should eat less meat, but that's a personal decision, and one that shouldn't be forced on anyone.
I'm not sure if everyone becoming vegetarian would cause the outright extinction of foodstock animals, since cattle and most forms of poultry can still manage to live in the wild, but it's a silly proposition none-the-less.