If you look at the balance sheet of a central bank, you will see it has liabilities (mostly currency) and assets (normally mostly government bonds/bills). Why do central banks have assets? Do they need them?
The wrong answer is that central banks need assets to "back" the value of the currency, and that paper currency would be worthless otherwise. The right answer is: since the government gets all the profits from a central bank anyway, there's no point in giving the government the assets; that owning assets lets the bank reverse course and reduce the money supply if it ever needs to; and it stops the accountants freaking out.