Those in thrall to the current transgender fashion sometimes give the impression that they believe that one is what one says or thinks one is, but this is clearly nonsense. Just because someone says they're a tree or even genuinely believes they're a tree it doesn't follow that they are a tree.
Others give the impression that they believe that if a man, say, identifies as a woman and dresses like one that that makes him a woman, which is also nonsense. If someone thinks he's a space alien and dresses like a space alien no one else thinks he really is one, no matter how adamantly he insists that he is.
Still others apparently believe that if a man believes he's a woman and has himself surgically altered and has estrogen treatments that that makes him a woman, but being a woman is more than having superficial secondary sex characteristics.
A woman is born with two X chromosomes and either has at birth or will develop during puberty all the appurtenances thereunto. She is born with a uterus, fallopian tubes and a pair of ovaries holding a million ova.
She has a history of developing her secondary sex characteristics and beginning menstruation. No man has that history, and if a woman who claims to be a man does have that history she's not a man regardless of what she thinks.
Moreover, a woman has an entire suite of chemical hormones in her body that men don't have and do not obtain simply by having themselves surgically emasculated. A few of these are follicle stimulating hormone (FSH), which stimulates the follicle to ripen, luteinizing hormone (LH) which orchestrates the menstrual cycle and estrogen, which a female body produces naturally.
Other hormones are produced if an ovum is not fertilized which allow the body to discharge the corpus luteum, but if fertilization were to occur, if a male-identifying female nevertheless became pregnant - the state of affairs that causes some to claim that "men" can become pregnant - her body would produce a host of other hormones which would guide the pregnancy process. An actual male body can produce none of these. The list includes progesterone, human chorionic gonadotropin, relaxin, placental lactogen, oxytocin, prolactin, etc.
In other words being a man or woman is far more complex than one's psychological state alone or one's superficial appearance or anatomy. The differences are deeply-rooted in our genetics and physio-chemical makeup.
Individuals should be free to decide to let their psychology trump their biology, but no one should think that he or she has the right to demand that everybody else go along with that decision.