Your point is crystal clear and speaks volumes.
As my Dad used to say about people who wanted to debate a moot point such as you have pointed out... "they're just bull$hittin' themselves."
It is possible to be female and have a Y Chromosome or be male and have 2 X Chromosome.
Your Gender is determined by how much estrogen or testosterone you have at a certant vital stage of your development in the wound. If your mother for example produces a huge amount of estrogen or testosterone at that time.
You will be born anatomically a woman or man regardless of your Chromosomes.
What makes a man a man is his male reproductive organs and a woman a woman her female organs.