Not sure I agree with all of this.

"man" and "woman" seem to have sociological definitions, while "male" and "female" are biologic ones. Last data I recall stated that 99.87% of born individuals unambiguously contain reproductive organs which, if functioning properly, produce one of the two possible gametes. Based on that, it seems to me to be rather easy to define "male" and "female", because in biometrics, you would never allow statistically insignificant deviations from the norm to invalidate a rule.

The debate (such as it exists) to blur the lines between male and female is thus either a straw man or a reductio ad absurdum, depending on how you look at it. Some attempt to argue because in a somewhat larger number (1.7%-ish) of live births sex is *visually* ambiguous, the lines blur: but, in such a situation, a look "under the covers" with an ultrasound of the pelvic region displays the profile of either one or the other reproductive systems. Others attempt to argue that the proper *functioning* of the reproductive system is necessary to avoid ambiguity, which is nonsense prima facie.

And, then, of course there is the nonsensical argument that because 99% (probably an under estimate) of the population is visually ambiguous (either by intent or by nature) as adults, we should just toss out classification altogether (which would require tossing out modern biological science, but I digress.)

So, although I concur that this are also archetypical categories, I think we can still say that in this case, rigid categories still exist.