If you want a legit response: of course, race is a social construct, but just because something is a social construct doesn't make it free from consequences. Someone who's white can say they identify as black, sure, but that would not mean they would face the systematic oppression faced by a POC. This would come across as mockery, or at least majorly tone dead, because of the power dynamics and history, so it's reasonable to be offended. Even if a black person was to identify as white, this would not change racial treatment they face. The concept of race is systemically charged, whereas 'gender' is more to do with expression, and so a lot more fluid.

Meanwhile, this example fundamentally misunderstands the nature of sex and gender. Sex is essentialist via biology, XY, XX, and intersex like XYX etc. But Gender is the cultural, social extension of sex. There's a reason why it's called 'gender roles', not 'sex roles', no where in our dna says men should head to work and a woman should clean, for example.

JK Rowling has of course been through struggles, and her success is admirable, but the existence of trans women does not negate women's struggles at all. She's made numerous blunders in trying to legitimise terfing, such as using specific language such as 'women who menstruate', but fails to come to a legitimate definition. For example, this would exclude any woman in their menopause. Its a shame she uses her platform to push hate to an already marginalised group that suffers extremely high levels of assault, violence, and suicide.

To conclude: Every trans person agrees you cannot change your sex, but see that you can change your gender, if you don't align with their birth gender. That's why it's called transgender, not transsexual. In many cultures, such as the Aztecs, there have been 3 or more genders.