Simple answers are convenient, glib, easy to remember and typically wrong.
Interestingly, so are overly complex, turgid, incoherent babble answers, which ultimately do not mean anything.
Humans belong to a species of primate, a type of mammal, and like all primates, our species have two sexes. Not three. Two. Human psychology may certainly "identify" as infinite things, and there are people who identify as animals, fantastical creatures, things they call genders like "paleogender" or "ambigender" or "gender queer" or "gender outlaw" or whatever, and sure, some humans have a psychological aspect where they believe they feel like a woman or a man when they are male or female, and some say they feel like both, some neither, some alternating, whatever - these are not sexes. These are psychological identities. It's fine to have them. They may be dysphoric about it, or maybe not. But, they are not a different sex. And that's ok. They are still humans. They are still people. Nobody is "erasing their existence." They are free to self-identify as whatever they want.
Me? I am male. i do not "identify as male." I am male. Biologically. If I was in an accident and put in a coma, I would still be male. When I die and get put in the ground, and archeologists dig me up in 500 years, they will see that I am male. It matters not what I think about it. I do not identify as any gender identity. I am not "cis" gender. I am only male. My only "identity" is who I am - my name is [first and last name] and I have a complex personality of moods, mannerisms, tics, proclivities, predliections, desires, faults, qualities, whatever. That's my identity. I do not identify as a man. I am a man, defined as adult human male. I cannot say how a man or woman feels -- nobody can - be cause we only know how we ourselves as individuals feel.
We can certainly feel more or less manly. We can feel more or less masculine, as those terms are defined in our language, but that isn't what makes one a man or woman. Although I am male, I have a fondness for cooking, and for cleaning the house, and I like to go grocery shpping. These are tasks normally associated with women. But, I dig them. Am I a woman, then? According to the gender ideology, the answer to that question is "if you feel like a woman, yes" - I am not a woman because I meet any particularly criteria - according to the gender ideology folks I am a woman if I say I feel like a woman. So, I can be and act very very manly, but if I say I feel like a woman, then I'm a woman. That's fine, I'd be free to do that, but it still doesn't change my sex.
Since one's gender is not testable - it's not determinable by anyone watching me, examining me, or running any test. Nobody can look at my brain or dissect me, or check dna, or anything and determine my gender - and since the only criteria for knowing a person's gender is their psychological self-identification, it's no different than any other part of our personalities. A person who feels like a woman feels womany (however that person individually feels). I.e., one person may feel what the dictionary definition describes as hypermasculine and another person may feel what the dictionary definition describes as hyper-feminine - both of them may "identify" as a woman or a man, or both or neither, or alternating. And they're free to do that, but none of it makes any objective sense. The words have lost all meaning, because they only mean what any individual person says they mean at the time and those meanings are subject to constant change.