Properly enacted, independent thinking is not in the service of self-will or subjective opining, but in the service of submission to a higher authority, truth herself. We think for ourselves in order to find a truth that is not from ourselves, but from reality. The idea is to become dependent on reality, rather than on institutional and social distortions of reality. Independence subserves a higher dependence.
It is worth noting that thinking for oneself is no guarantee that one will arrive at truth. Far from it. The maverick's trail may issue in a dead end. Or it may not. The world is littered with conflicting opinions generated from the febrile heads of people with too much trust in their own powers. But neither is submission to an institution's authority any assurance of safe passage to the harbor of truth. Both the one who questions authority and the one who submits to it can end up on a reef. 'Think for yourself' and 'Submit to authority' are both one-sided pieces of advice.
And you thought things were easy?