stick - but this is the issue.
Legally, you can be recognised as male if you identified as female at birth, or female if you were identified as male at birth.
A very small number of people are born with intersex conditions, for what it's worth - I'll note that because people always do in these debates, though transsexuals are not people who were born intersex, or not typically (it's very, very rare).
The legal situation, then, doesn't relate to whether you have XX chromosomes or what genitalia you have. It is possible also to have surgery that could give someone who was born with a penis something that looks more like a vagina, or vice versa.
Obviously, chromosomes are hidden, so some people would say, look, it doesn't matter what the genetic coding is, what matters is how you feel inside. Some people have a strong internal sense of their 'gender identity' and reckon they know inside whether they're male or female. Others don't have this. Others again - including lots of radical feminists - think even this internal sense of 'gender identity' might be the result of social conditioning.
Most of the time, obviously, it is perfectly possible to be respectful of whatever other people think, because 90% of the time there is absolutely no reason why anyone needs to insist 'well I shall use gender identity to categorise everyone as male or female', or 'well I shall use chromosomes'.
Occasionally, it starts to matter to some people. For me personally, I don't like to be labelled a 'ciswoman' because that qualifies 'woman' in a way I find othering and offensive. And I think it matters to be able to discuss issues to do with having a female reproductive system with other people who've grown up with a female reproductive system (and to me, that includes women who've since had hysterectomies, say, because I think their formative experience is the same). But now we're getting into the personal side of things.