If psychological continuity were sufficient for personal identity, both post-fission branches would be identical to the original, making them identical to each other — a contradiction.
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psychological continuity(Philosophy of personal identity)
A relation holding between a person at one time and a being at a later time when the later being inherits the memories, intentions, beliefs, and psychological states of the earlier person.
sufficient condition(Used in the context of whether intrinsic properties can define species membership)
A property whose presence guarantees membership in or applicability of a category, such that having the property entails belonging to the species or class