The problem of personal identity is really a problem when you have not any reason for claiming yourself a definite identity, especially in the social context.
For a real problem is only one that leaves just a tiny space for escaping from an obstacle or difficulty. And those who have a comfortable and definite social status leave in fact a little space for doubting their identity.
The problems of personal identity circles the questions: Am I a soul or rather a body? Am I an eternal being or mortal as any other animal? Am I a moral person or not?
A priest, preacher, or teacher of morality is already someone who has a clear identity and his answers to the previous questions cannot be trusted, since we have serious reasons for doubting his sincerity in putting them.
Meanwhile, those who have not a social identity rather feel those questions than think of them. Thoughtful and introvert persons have not such identity. They are felt because each question seems to accuse them for their incapacity of creating a social identity. In virtue of this feeling, their answers would be worth of being listened, in spite of the common despise for any unfitted persons.
However, it is a painful experience to confront an accusation and, for this reason, many spare the questions and refuse to formulate answers by preferring to trust in the answers given by those who did not really questioned themselves about identity.