This is definitely not true. I don't understand where this assumption came from and I cannot logically follow it through. Certainly 1) not 100% of building heights are livable space, and certainly 2) you cannot just extend one dimension of life (building height) and then assume that you will have created some economically usable housing.
> If there were twice as much housing, there wouldn't be a shortage
Again I don't understand this at all. The shortage isn't about the amount of available housing at all, it's about people's ability to live there too. And if you're just doubling the building heights, you haven't talked about wages or ability to live there etc.
> It's really quite straightforward
What? None of this is straightforward! This stuff is super complicated! There's no need to be so condescending and rude about it.
> Which part of the argument do you think is incorrect, and why?
All of it. I've explained above.