[selcuka]

> I wonder if the origin of the question is the religious idea of a separate immortal soul

I don't think so. This is a profound question in philosophy, and it may even predate religions, even though it is hard to separate philosophy from theology. The answer (if there is one) doesn't have to be metaphysical.

Also the question is not about your genetics, your character, or "being someone like X" per se. Your twin brother could be genetically (let's say 100%) identical, but still you are you and he is he. There is only one "I" and everyone else is, well, other people. Being "I" has nothing to do with my experiences. No matter what I will experience in the future, I will still see the world through the same pair of eyes.

If you change the question from "I vs someone else" to "person 1 vs person 2" it stops making sense. From your point of view "p1" and "p2" are interchangeable and you wouldn't know which one is which. When one of the subjects is "I" then the symmetry disappears and the vertiginous question appears.