The phrases “assigned male at birth” and “assigned female at birth” are commonly used today to reflect the idea that a child’s biological sex is not necessarily their ultimate gender identity.
These terms hinder clarity instead of adding to it. Much better would be “assigned boy at birth”, and “assigned girl at birth”.
There are two biological sexes, with true intersex conditions a tiny minority. A much larger (but still very small) proportion of people will discover/choose a gender identity that does not match their biological sex.
The vast majority of the time, sex and gender are fully aligned throughout life. When there is a misalignment, what is it that it turns out was misassigned at birth? Gender, not sex!
If the penis and scrotum that were observed on an infant at birth have transformed themselves over the years into labia and the associated internal organs, we might say that the assignment of ‘male’ at birth was incorrect. We might also say this if female physical characteristics have arisen at puberty that suggest a reality that trumps the perception at birth of a penis. But this is not the sort of error that people actually intend to convey with “assigned male at birth” with the associated implication that it might have been wrong.
The mismatch they speak of is in the mind. Setting aside these terminology choices, a few children might say, “People observed at birth that I had male genitals, so they assumed I was a boy. But I have discovered that I am not a boy.” Summarizing that as “assigned boy at birth” is far more accurate than “assigned male at birth”.
When my alternative formulation is accepted, we will be lucky that the words male, female, boy and girl all start with different letters! Instead of AFAB and AMAB, we will have AGAB and ABAB.