Well as a simple matter of fact, banks don't have the right to print banknotes, they merely create electronic deposits and then if someone wants to turn those into banknotes the banks have to borrow them from the Fed (or local equivalent). The more important difference this represents is that money is "created" as loans, with the bank's profit being the difference between the total amount that gets repaid to the bank by some creditworthy private person or organization and the amount the bank owes the Fed. So (i) the bank doesn't get to spend the money it "creates", it's actually reserves the bank owes to whoever's deposit account the money ends up in and (ii) it's a market-driven process where the bank is only incentivised to create money if prospective borrowers are demanding loans and the bank believes they will be able to repay them. (And the Fed in turn, "creates" and "destroys" money to the extent necessary to ensure the market interest rate is at a desired level, not to make profits or pay bills)

The uninformed school of internet libertarianism likes to conflate this process of credit creation with the practice of unstable governments realising they'll never be able to raise enough money from taxes or oil sales to pay for the mansions and five star generals they'd like to buy and so printing some more banknotes (not owed to anyone) to be a bit richer.