Forget theory, ideology, and politics for a moment. Let's focus on the mechanics of how things work.
When a bank lends money to a company, the bank and the company book corresponding accounting entries and money is created "out of thin air." (The bank is required to hold a minimum reserve balance, which they can borrow as needed from others in the financial system, or from a central bank).
When a central bank (like the Federal Reserve or the Bank of England) lends money to a bank, the central bank and the bank book corresponding accounting entries and money is created "out of thin air." Central banks literally click a button and create accounting entries.
When you borrow money from a bank, the bank books the corresponding accounting entries, and you probably won't record anything on an accounting program -- but your bank will keep track of all balances, to the cent.
When a borrower cannot pay back a loan from a bank, the bank writes off the loan balance, and reduces the borrower's liability by an equal amount.
The balance you have on your bank account is a liability on your bank's accounting books.
The balance on your credit card is an asset on your credit card company's accounting books.
When you buy something and pay with a check or a debit card, the financial system records all the necessary accounting transactions to update everyone's debit and credit balances.
The dollar bills you hold in your wallet are nothing less than 'certificates' indicating that the US government has a liability of the amount shown on those dollar bills, payable to the holder of those dollar bills.
In our modern economic system, the easiest way to understand money is as a global, mostly electronic network of accounting debits and credits, with balances varying as people conduct transactions.
For every debit there is an equal credit, and vice versa, so globally, total debit balances are always equal to total credit balances, and total debit transactions are always equal to total credit transactions.
Double-entry bookkeeping all the way down.
It is really quite something to behold.