Lets say that one family (two adults and two children) eat one animal/week. That's a very conservative figure, right?
That's 88,088 billion animals in one year, or 242 million animals/day.
And we remember, we take them from the wild. There are no farms with tens of thousands of pigs or cows.
Furthermore, you want to let the human population naturally increase in size. It won't take too long before we're packed like sardines, so not much room for nature anymore. Not that that would ever happen, humans will start dying by the millions once the food starts running out.
we could still have farms. people could raise their own food instead of relying on applebee's chicken nuggets for dinner every night.