So I did a bit of maundering on what bugs me about Objectivism, and I think that I can sum up my chief objection in one sentence: My hair was dark brown, and is now dark brown and gray. Yes, it's still hair, but it is not the hair that it was. If we consider the physical person as A, then A ceases to be what A was, as one grows older. If this was untrue, we all would still be small bald wrinkly persons wearing diapers, wouldn't we? Alternately: Italy WAS the seat of the Roman Empire, but IS no longer. A ceased to be A, didn't it?
If you're someone who finds that Objectivism fits your worldview, please DO point out what you see as the logical fallacy here. I'm not seeing one, but that doesn't mean there isn't one.