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I thought private banks create money the moment they take out a credit from the central bank. The central bank's job is to set the interest rate for those loans, et viola.

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That's one method, but consider what happens when someone deposits a million dollars at a bank. This million dollars can be lent out to another person as a mortgage, and guess where that person accepts that money? That's right, a bank. That same 1 million dollars could be lent out to 10 different people, expanding the supply of money many times over. The only limit to this are the capitalisation ratios legislated and enforced by government (the bank must retain some % of total outstanding liabilities as capital it can move immediately). There are a few other ways I understand (and probably many more I dont) that the monetary supply can be expanded via, but that is the simplest one to conceptualise.

"This million dollars can be lent out to another person as a mortgage"

It can't. It isn't. And it never has been.

What banks do is provide liquidity against your collateral. You sell them a charge over your house (for example), and they give you a credit for it. That credit can then be passed on to other people.

Banks are in the business of discounting. They don't take anything in and give it out to other people. [0]

[0]: https://www.bankofengland.co.uk/quarterly-bulletin/2014/q1/m...

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