According to Socrates, an unexamined life is not worth living. Call this the Socratic view. Some would disagree with the Socratic view, insisting that an unexamined life can be flourishing, fulfilling, satisfying, happy, valuable, meaningful, and hence worth living. Call this the other view. I think the other view is correct, but there is a way of understanding the Socratic view so that it is compatible with the other view.
The Socratic view should be understood against the background of the question "How should I live my life?". Call this the Socratic question. Anyone can ask the Socratic question, but not everyone does ask it. But for a person who has asked the Socratic question, the only way to answer it is to examine her life so far and see how she should move on (or whether she should move on at all). To put it another way, a person who has asked the Socratic question is already self-reflective, and her attempt to answer it consists in having further self-reflection. If she finds an answer to the question and knows how she should live her life, that must also be a life that she thinks is worth living.
The Socratic view is thus true for a person who has asked the Socratic question, for it means no more than that a person cannot answer the question "How should I live my life?" and say, earnestly and firmly, "Yes, my life is worth living!" without having examined her own life.
On this understanding, the Socratic view is thoroughly first-personal. The other view, by contrast, is third-personal. It is possible for a person's life to be considered worth living by others while he himself does not have the belief that his life is worth living because he has not asked the Socratic question.