If you were to be perfectly duplicated in every respect, would the duplicate be you?
Intuitively, the answer is no. I'm me, and the duplicate is the duplicate. But intuition is not perfect. Our intuition is a shortcut rule-of-thumb for life on the savannah. In a radically different environment, or different circumstances, intuition is not a helpful guide at all, and can easily lead you astray.
Consider, for instance, relativity. If you see one person running at six miles an hour in one direction, and another person running at six miles an hour in the other direction, what speed will the first see the second one going? Intuitively, and correctly, twelve miles an hour. But what if you see one spaceship moving at 2.9x10^8 meters per second, and another moving the same speed in the opposite direction? Will the one spaceship see the other moving at 5.8x10^8 m/s? No, it will see it moving at 2.999x10^8 m/s. Because velocity addition is not really u+v as we intuit, but rather (u+v)/(1+uv/c^2). It's just that at low speeds, the speeds we evolved with, the difference is imperceptible.
And similarly, we never evolved in an environment where people were perfectly duplicated. Our intuition isn't equipped to deal with that situation. So to answer that question, we can't rely on our intuition. We need something more than that.