Zoning has a lot to do with home sizes. In general American cities are zoned to not allow smaller units, even for those who might prefer the cheaper rent if given a choice. Japan has much simpler and more flexible zoning laws.

...But Japan doesn’t have the history of racially motivated urban design in general, so the story is a bit complicated.

That, and America has been heavily subsidizing an automobile-based lifestyle for 60–70 years, encouraging people to trade more living space for longer commutes, without facing the full infrastructure costs of the choice.