I do agree that saying a trans man was “born female” is very problematic—unless he did identify as a girl at the time. But the discussions over terms like “bio-female” seem to be a little more complicated. I’ve heard the argument that there are many variables within biological sex, so many that it shouldn’t even be considered a binary system. While it’s true that primary and secondary sex characteristics do vary, and that there are plenty of people whose genetics do not determine their sex in a predictable fashion, I still think it makes sense to think of “male” and “female” as biological trends. The problem arises from our use of the same words to mean two different things. “Male” applies equally to gender and sex. A biologist would use it to mean an individual with XY sex chromosomes who develops certain secondary sex characteristics due to certain levels of hormones present in the body. “Male” here is a biological pattern. Most, though definitely not all, people with XY chromosomes develop in a similar fashion. It is erasing to claim that there is only one way for people with XY chromosomes to develop, as there are people with “male” genotypes but “female” phenotypes, but it is a fairly regular pattern.
Of course, “male” as used to describe gender has a different meaning. Yes, there is often confluence between the sex of “male” and the gender of “male”, but they do not carry the same definition. The gender refers to an identity that tends to include certain behaviors and aesthetics. It’s a pattern too, but one that has less to do with biology.
So how do we reconcile these two definitions hiding within the same word? Is it wrong for doctors to stamp “male” or “female” on birth certificates just because a baby exhibits a certain phenotype?
Personally, I don’t find it terribly problematic that doctors and parents predict a certain biological future for their child based on the appearance of their genitals at birth. If a baby has a vagina, it's likely (though not certain) that it will one day begin to menstruate. What I do find problematic is that new parents are rarely informed of the difference between gender and sex, and the possible discrepancy between the two. Doctors probably shouldn’t declare “it’s a boy” upon seeing a penis, because let’s be honest—they don’t know yet. “Boy” is a category dependent on more than just biology. What they should say to parents ought to be more along the lines of “it’s statistically probable that your child will develop and identify in a certain way, but don’t count on it.” Maybe if we stop assuming identity follows biology, we’ll make some progress in how we as a society conceive of gender. And while we’re at it, we should find some better ways to linguistically differentiate “male” the biological sex and “male” the societal gender. While they usually go together, they are certainly distinct enough to warrant different terms.