Question

why the courts and judges should be independent of state and central government authorities

Answer 1

So that they would be able to take decisions independently in the favour of the nation..
It is vitally important in a democracy that individual judges and the judiciary as a whole are impartial and independent of all external pressures and of each other so that those who appear before them and the wider public can have confidence that their cases will be decided fairly and in accordance with the law.
hope it may help u

Answer 2

So that none of the ministers would pressurize the court for misleading