I believe you are misconstruing self-identity. As Heraclitus says, you can never step in the same river twice, though paradoxically, we can refer to "the river" and conceive of "twice."
Similarly, we can point to "that same stone." Yet the stone is never "the same" and never isolated from "non-stone" forces that ceaselessly change it over time and space. For the stone, there is no "being itself," nor what we would call "freedom" from external forces and mechanical causality.
The self-conscious being, on the other hand, by definition entertains a concept of "itself" and the contradictions that define it by what it is not. Without this irreducible contradiction, we would not have desires, uncertainties, or entertain possibilities apart from what merely is.
Like the stone, we will constantly change, becoming other than we are or were. Yet we have presumably a capacity for freedom, a kind of second-order causality that allows us to pry apart and suspend mechanical causality and actualize the possibilities therein.
Obviously, Hitler can never "really become" Florence Nightingale, since these are particular and mutually exclusive subjects. But Hitler can access his subjectivity to be other than he is. This, at any rate, is a basic interpretation of what we mean by "freedom," though of course there are various determinists who would argue that we are subject to fate, destiny, or a physical determinism little different from the stone's.