>> If you withdraw it in cash, then the bank will have to give you some of the Federal Reserve Notes it has in its vault
And while that is indeed technically true, it only applies to money withdrawn as banknotes. Given that most of the economy is electronic transactions, that loan is to all extents and purposes real money created by the bank out of thin air (modulo capital requirements to back debt).
I address electronic transfers in the next paragraph. Even if initially transferred only within the bank, it is likely to eventually be transferred to another bank, which requires the bank to transfer corresponding reserves to that other bank.
Only the Federal Reserve can create truly unlimited amounts of money without the risk that customers might request transfers that exhaust their reserves.
Complying with reserve requirements imposed by the Federal Reserve on banks help to mitigate this risk, but they are not the true restriction. Even if the reserve requirement was zero, banks would need to keep some reserves or they would be completely unable to fulfil requests to transfer funds to other banks. And even if a bank exceeded the reserve requirement, for example by keeping 50% reserves rather than 10%, they would be insolvent if customers requested 51% of balances transferred out and were unable to cover it with loans from other banks.
And while that is indeed technically true, it only applies to money withdrawn as banknotes. Given that most of the economy is electronic transactions, that loan is to all extents and purposes real money created by the bank out of thin air (modulo capital requirements to back debt).