Your definition is okay, but I would go with a human being whose twenty-third pair of chromosomes (i.e., the sex chromosomes) are XX, while a man is a human being whose sex chromosomes) are XY.
The reason that I would go down to the DNA-level like this, is that, sadly, a small number of genetic freaks out there who have, for example, XXY or XYY sex chromosomes and are hermaphrodites whose sex organs can get very weird. As such, I’m not totally comfortable with a definition of womanhood that says you’re a woman if you have this or that “part.” No, you might have that particular part and be a hermaphrodite. In reality, though, we’re talking about a very tiny segment of the human population, estimated 0.02% to 0.05%, that can’t clearly be classified as man or woman.
You can have the normal xy scenario for your sex and still have weird issues with the things that make you a man or woman when someone looks at you ..such as with Congenital hyperplasia.
You then look to the chromosome...but should you....I can’t answer that but I can see why one be might identify as different sex with such an issue..
Again this is different than the clearly dude swimmer who decided to be a woman