The reason for central bank independence is that monetary policymaking under the influence of politicians tends to focus too much on short-term considerations. This can easily lead to temporary, non-sustainable increases in growth, but inevitably results in lasting increases in inflation with no lasting gains in growth and employment at all.
Politicians all over the world have come to realise this and have decided to remove the temptation to pursue short-term gains and to make their central bank independent. It should be underlined that granting this independence is, as it should be, a political decision. An independent central bank needs a clear legal mandate.