I remember being shocked at some point that my deposits at a bank would actually be a liability on their books not an asset. When you think about it as passing around debt, it makes a bit more sense.
The easier explanation is that your deposits are yours, not the bank’s. In terms of debt, they owe you. They make money by borrowing from you and lending long term debt to get more yield than they pay you on your cash (you may hear this called “borrow short to lend long”).