Maybe it doesn't and there is a plausible explanation, that's why it has been an unanswered question. But it's definitely an astonishing question.
You instincitively say that even if you duplicate the whole system "you" would remain as "you" (or "I", from your point of view), and the replica would be someone else. In this context you claim that there is a new consciousness now, but there was supposed to be one, because our initial assumption was consciousness == brain.
You are right if you define consciousness as being able to think, but when you define it as what makes you "you", then it becomes harder to explain who the replica is. It has everything (all the neurons) that makes you "you", but it is still not "you".
The above may not make sense as it is difficult for a layman such as me to explain the vertiginous question to someone else. I suggest you to read the relevant literature.
Im probably lacking in imagination, or the relevant background, but I’m having trouble thinking of an alternative.
You assume that both would feel like you, but there is no way you can prove it. The other can be a philosophical zombie [1] for all you know.
Would the "current you" feel any different after the duplication? Most people, including me, would find this counterintuitive. What happens if the other you travels to the other end of the world? What would you see? The question is not how the replica would think and act from an outside observer's perspective, but would it have the same consciousness as you. Would you call the replica "I"?
Or to make it more complex, what would happen if you save your current state to a hard disk, and an exact duplicate gets manufactured 100 years after you die, using the stored information?
Thanks for the additional explanation. I have read a good deal from Nagel to Chalmers and somehow missed this particular question.
Chalmers' "Hard Problem" is very similar, although not exactly the same. My understanding is that it asks "why is there something called consciousness at all", as in, a robot doesn't have the notion of "I", but for some reason we do. The question is hard because it is hard to explain it only by our brains being more complex than a robot's CPU. Hellie's question is "why am I me and not someone else".