Factory farming uses almost no land. The animals never leave the building or their cage.

I don't quite get the point you are making. Can you rephrase it?

You can't plow a mountain side and grow acres of corn or build a feedlot. But you can run cattle and sheep over it which are able to forage the grasses while climbing the terrain.

So mountainous people are able to obtain calories from animals in places otherwise unsuitable for more conventional farming methods.

No one is trying to force people to abandon their locally sourced food. The problem is with people in developed nations who live in cities. Also the point is you wouldn't need to expand the farmlands, quite the opposite.

Thanks for clarifying.

Letting cattle and sheep and goats forage in terrain unsuited for agriculture is fine.

I still think we should stop feeding that 1/3rd of our grain to cattle.