By issuing deposits, each bank creates essentially its own money which is valid as long as it is inside the bank (used in transactions with other clients that use the same bank), but when clients send money to other banks, the bank has to use 'central bank money'.

Which means banking system as a whole creates 'private money' when flows of 'central bank money' between banks are balanced, but each individual bank cannot do it faster than others, otherwise these flows will be negative and it will be losing 'central bank money' and/or hard assets (which would be sold to acquire 'central bank money').