Why don't we say this about other expenditures? Am I throwing my money away when I buy dinner and not a cow? Did I throw my money away by buying a carrot and not farmland? I don't think the statement is true or false, it's just meaningless.
The oft-repeated statement that "renting is throwing your money" is an implicit contrast to owning a home, where the mortgage payment "builds equity" in your asset that can be sold later.
"Throwing money away" means you don't get to own something that can be sold for money later on. That's why we "throw money away" on gasoline, but not "throw money away" in a savings account.
The second part of my argument is that throwing money away isn't necessarily a bad thing, because the alternative (such as paying to own something) can end up being more expensive and being a worse deal financially.
I've never heard someone claim I am throwing away money when I buy something consumable except rent. It's a stupid statement that doesn't convey any useful information.
How is it foolish to spend money on housing?