Anatta, I think this should be on the Philosophy board!!
It seems that the underlying issue in one of contiguity or continuity. Parts of our bodies are "original issue." Other parts (i.e. blood cells, etc) are being constantly replaced. Yet, we retain a sense of unique identity.
Decartes noted Cogito ergo sum, "I think, therefore I am." If my essence is derived from my sense of self, rather than from the bundle of tissues comprising my body, than I remain the same, even as I physically or intellectually grow.