The importance of transaction symmetry in an unlimited credit system

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"Money creation in the modern economy" by the Bank of England

tl;dr: When banks lend money, they don't use existing customer deposits for this or loan money from the central bank - they simply extend their balance sheet by that amount - with the newly created money on the borrowers' side - visible to them as a deposit, and the value of the loan to the other. They effectively create money out of thin air.

Liquidity becomes relevant however when the money leaves the bank - when the borrower transfers money to another bank (as payment for example) or withdraws cash. Here the bank has to ensure it has sufficient central bank money, cash or assets it can convert to the former in order for this and further outflows to take place. So the distinction between book and real money is essential.

Note: If the borrowed, book money is used to pay a customer of the same bank, it works perfectly, because the money doesn't leave the bank.

Only a central bank can create real money out of thin air by either printing it or increasing its database entries because both of these count as real money. Banks transfer value between each other using this real money.

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This is something I haven't found being explained elsewhere:

Introducing Alice at Bank A and Bob at Bank B

Alice wants to transfer some money to Bob, and Bob some to Alice. Naively, both banks could physically move cash or transfer central bank account money between their central bank accounts via RTGS.

A better idea, especially if there are more customers who send many small transactions between the banks, are Net settlement systems. Instead of transferring each small transaction individually, both banks wait until the evening, then sum everything up, and only the bank who owes the other more conducts a real money transaction to the other.

This works even better when the amounts transferred between banks always sum up to 0 - no real money whatsoever has to be moved.

Now imagine this situation:

Bank A and Bank B start with $1000 of their own money each.

Now both Alice and Bob borrow $2000 from each bank. This would cause a bank run if they tried to withdraw it, or only one side tried to transfer all of their borrowed book money to the other bank. But it works perfectly when the situation is symmetric, when the transfers in both directions sum up to 0 again (or below $1000) (and the repayment ability returns in the long run).

So a "symmetric" banking system is able to create more credit, because less real money is required to maintain sufficient liquidity.