This is true for me, too. I am a woman because I am female mostly the way I am a certain height and a certain age. They are facts about me, and not my identity in some abstract sense.
Though being a woman is different from being a certain height, mostly, because of some of the consequences, such as experiencing sexual harassment, an attempted rape, discriminatory treatment at work etc.
Because of this, I identify WITH other women and girls, but this is not the same thing as what the gender identity ideology describes.
It's possible that transgender people define the way they feel as being the same as some universal gender identity which may not always happen to coincide with the sex a person is, but I don't share that explanation, though I am willing to accept that they have feelings which they describe in such terms.
Whether the society should respect people's stated gender identities is not as simple a question as it might seem for those who wish to be kind or inclusive, because in other areas the society does not respect all identities when they cannot be externally verified.
For instance, we can't identify as some professional if we don't have the qualifications for that, and if we tried to identify as a different age than we are, others might find that exasperating and possibly refuse to respect that identity in situations where age would matter. So it's not necessarily true that the individual alone can determine how the rest of the society treats their stated identities.