Banks are part of the state or there is no insurance

If both of the following are true then banks are part of the state and print money: i) banks are guaranteed by the central bank ii) the central bank is guaranteed by the state. If either (or both) are false then banks do not print money and are not part of the state.

These two statements can’t both be wrong... only one is correct: Either there is no valid deposit insurance for the banking system (deposit insurance is unreliable) or banks print money.