It should have been "woman" or "man", male and female are fixed and we need more education if people are confusing the gender with a constant.
Unfortunately and regrettably, this whole area is one big mess.
And it's a mess because historically, society has entirely conflated gender and (biological) sex. "Male" and "man" have been treated as perfect synonyms, as have "female" and "woman".
The medical and academic communities, ever since they've reached the understanding that gender and sex are actually
not one and the same, have adopted the (sensible) terminology of using "woman"/"man" for expressions of gender identity, and "female"/"male" for sex. And this separation makes it possible to have a clear, unambiguous understanding of the subject.
However, in the real world, things are hugely more complicated. For example, take the matter of passports. Passports have a field in them under the heading "Sex", with the options "F" or "M". And this throws up a big problem where it comes to transgender people. If passports were to follow the medical/academic terminology, a transman would have "F" in this field, and a transwoman would have "M".
However if that were the case, not only would transgender people view it as - reasonably, IMO - a form of denial of their transgender identity, but also it would have the clear potential to cause problems/misunderstandings/prejudice* at border crossings, where border officials might (eg) see "M" on the passport, but see someone presenting as a woman standing in front of them.
Another example of a problematic area is to do with criminal law wrt verbal abuse of transgender people. In most progressive jurisdictions that are introducing legislation to protect transgender rights, the legislation cannot stick rigidly to the medical/academic separations. Rather, the relevant laws deliberately - and entirely correctly IMO - make it just as grave a criminal aggravation to abuse (eg) a transman by calling him "(a) female" as to call him a "woman".
As things stand right now, in late 2021, all the stakeholders in this subject matters - including legislators, regulators, judiciaries, the media, transgender people, and society at large - are still slowly trying to navigate their way bit-by-bit towards a workable and fair consensus wrt definitions of terms. I suspect it'll take some time yet to reach an optimal point.