To be authentic is to accept personal responsibility for yourself – your whole self, your values, commitments, and identity, not only your actions. Accepting responsibility for yourself entails accepting that you are always free to do otherwise, or to put it differently, that whatever you did, you did not have to do it – you did it because you decided that doing it made sense for you.

To believe that you’re under some obligation to be authentic is, therefore, self-defeating. That, I take it, is what Sartre means by “for authenticity’s sake”: the idea seems to be that one just must seek authenticity because not to do so would be inauthentic. That authenticity’s claim is so strong that one doesn’t require a personal reason to seek it. A person joins the Resistance, for example, because it is what he must do – because not to do so would betray himself – not in order to be “authentic.”

Without going back to Notebooks for an Ethics, the source of the quotation, I can’t be absolutely certain that my interpretation is right, but I hope it is a start.