As social animals, we largely define our sense of self, our identity, in relation to others. This can be inclusive, "I'm similar to these people", or exclusive, "I'm not like those people". For most of us, our individual identity becomes an amalgam of all the different subgroups we identify with.

Now, pretty much the earliest group we get sorted into and identified by is based on our biological sex, which is normally determined/assigned at birth using our external genitalia. Once that happens, we start getting socialized to think of ourselves as belonging to one group or the other and how to present that identity in socially acceptable ways. For most of us, that works fine. For some, they feel like there is a mismatch between their physical characteristics (sex) and the social expression of that sex (gender) and their internal sense of which group they should belong to.

Ultimately, there is no objective, measurable criteria by which to judge a person's identity, because it is in their own mind. We can only look at what they say and do to determine how "legitimate" their identity claims are.