yeah, it falls out of how the brain functions i think... there are a bunch of classifiers in there, and its not always easy to map what they do to reasoning. there are loads of fuzzy concepts like this with day-to-day utility which are very difficult to define accurately in a way that unambiguously communicates intent to another person.
I suspect that identity is just another way of grouping things by properties, in this case including sharing spatial and temporal history - I am the same I was 10 minutes ago, because I'm made mostly of what I was made 10 minutes ago, and I moved somewhat continuously through space, etc.