When you wake up in the morning, when you have come from slumber to consciousness, you start the day with a subliminal awareness that you are the same person that went to sleep the night before. But how do you know you are this person? How do you know you are not someone else who happens to share the memory of the person from the night before?
Consider this problem like this. Suppose we could both clone people and implant memories. How would you tell each morning that you were the same person rather than a clone with identical memories? Presumably, you could not. But does that mean you only know who you are because you know that we cannot implant memories?
If our memory is the only way we know who we are, what happens when memory becomes suspect?