Imagine that God, or a scientist with some extremely sophisticated equipment, were to create an exact duplicate of me. Would I and the duplicate be the same person? Imagine that God could create the duplicate after my death, and the duplicate would have all of my personal characteristics, memories, beliefs, and so on. Would that person be me? On the surface, there doesn't seem to be any reason to deny identity here.
The problem arises with the possibility of another duplicate. If God could create one duplicate, the why not two? Then, both duplicates are identical to me. Identity is usually considered to be a transitive relation: If A=B, and B=C, then A=C. If both duplicates are identical to me, then they are identical to each other. Then, there the same person simultaneously occupies two different bodies. This certainly appears to be a paradoxical conclusion.