XY = Male XX = Female
XY and XX describe genotypes. Male and female (typically) refer to phenotypes. So yes, XY = the male genotype, but there is no guarantee about the phenotype you get with those (and only those) sex chromosomes.
If you have the XY chrom , you are a man. If you have XX chrom, you are a woman. These are just facts.
By talking about 'man' and 'woman', you are now talk about gender. You have left biology and entered the realm of sociology, like it or not. You are free to assert your own definition that 'man' refers to people that have the genotype XY, that developed into the typical male phenotype, and that never had any surgery or hormone therapies that would interfere with their phenotype. Nobody is compelled to agree with the definitions you're hoping for, though, and that definitionally isn't a "fact".
Honestly, the fact I have to point these things out is honestly mind boggling.
The main thing you're pointing out is that you don't have a sophomore's understanding of the topics.
The scientific community does NOT agree with this shit.
What "shit" specifically do you think scientists don't agree with?
Every one in the hard sciences thinks you people are batshit crazy.
I'm a cognitive neuroscientist at an Ivy. What are you talking about?