Central bankers normally operate on a longer term time scale than politicians and therefore do not face the same temptation to relax policy to achieve short-term objectives. By delegating decisions on interest rates and other monetary matters to such an independent institution, with a clearly defined mandate, society can then hope to achieve a better inflation outcome over the longer term.
The main criticism against making central banks autonomous entities is not so much based on economic but rather on political arguments: it is that turning over decisions regarding interest rates, exchange rates, the efficiency of the financial system and other monetary matters to a body of 3  BIS Review 34/2000  unelected officials is simply “undemocratic”.