> It's not uncommon for wealthy people to borrow against their stocks and then buy a home "in cash". In that situation, you'd never say "the bank owns their home" just because they owe the bank a bunch of money.

The difference lies in whether or not they can take your house away.

If you have a mortgage you're just renting until you pay in full. You don't own it until you fully pay.

If take a loan, and buy a house with the money, they can't take away the house. Sure, you could say that you might be forced to sell your house to pay back the loan, but that would mean nobody owns anything if he has to sell something in a pinch.