I would say that "a man" is someone who presents, or deeply wishes to present, in the way the society has generally dictated people who have been assigned male at birth have to. For example, I have a friend who is a trans man. I would class them as "a man", since they wish to present, and exist in society, in the same way that people who have been assigned male at birth would. As such, they have short hair, refer to themselves by a name that has more masculine connotations, wear clothes generally aimed as masculine people, etc
In the first case, take a law about pensions -- the law-writer wasnt giving masculine-presenting people fewer years of their pension than feminine-presenting people; they were applying it to adult males. This applies very generally across many uses of man/woman -- the speaker just doesn't mean masculine-people and feminine-people, even if that highly correlates with the people they did mean. (Taking masculine/feminie to mean those presenting-characteristics).
In the second case, consider the claim, "I am really a man!", if that's only a claim to masculine-presentation then 'really' doesnt make sense, right? How could an audience ever be mistaken about this? What is at issue when people claim this, or dispute this? No person who asks, "are you really X?" is disputing how something is already perceived as-being-X.
Compare with, "are you really a crook?", "are you really a police officer?", "are you really a witch?" In each case there is a literal, descriptive, perception-independent meaning.
One reply to me here is to bite the bullet and say, "I am really a man(, I am just perceived to be a woman)!" is meaningless. That claims, "I am really a man/woman!" are meaningless. That makes sense out of the view that it's all just social perception, but its kinda implausible -- because we've written so much using these terms that there's clearly a literal meaning.
Eg., consider going to the pension office to collect a pension at the age for which women are allowed it but men are not. You speak to the pension officer and say, "I'm a woman, so I'm allowed my pension now". It seems the pension officer can meaningfully dispute this, "Are you really a woman?"
If you asked, "what do you mean?" the pension officer could coherently say, "pension age for women is 66, meaning if you are female and an adult over 66 then you are entitled to.."
It would seem disqualifying to reply, "I am a woman because I am perceived to be the same as the people who qualify"
You can redefine the terms to eliminate any non-presentational meaning, but it seems quite implausible to say that the people who wrote that law mean to make it a choice as to whether you qualify for a pension.
When they said, "women qualify for a pension at age 66", they were not using the word "woman" which would have any sense of a choice associated with it, right?
Giving the terms "woman", "man" etc. only a presentational meaning renders a vast amount of our discourse using these terms absolute bizarre, at the very least. Law makers of 1940s setting pension ages were not handing the qualification criteria to individuals to decide, right? The law is not encouraging people to present-as-women, it's not saying: if you choose to present as adult females, we'll give you a few more years pension! Indeed, its hard to imagine any law-maker involved ever thought that qualification for a pension could turn on any choice an individual could make.
You can argue that people should not use "woman" to refer to "adult human females" in most contexts, or that it is better to take the rhetorical meaning of "woman" as the primary one (ie., the ones in which one claims to-be-like literal women) ---- but I cannot really see how you could claim the law makers of the 1940s were writing pension grants based on how people happened to present.
Likewise the same goes for medical textbooks, biology textbooks, etc. And a vast amount of social conversation. If bob says "I'm only interested in dating women", and eve replies, "I present in all the ways adult females do!", bob isnt mistaken to say, "no, i'm looking for someone to start a family with".
It's really really strange to say that when bob said, "i'm interested in dating women" he was confused when he thought being pregnant wasn't ordinarily entailed by the term "woman".
Again, you can try to change how these words are used. But the claim that lawmakers, doctors, biologists, ...people going on dates... that everyone is either confused or "always meant" making-choices-over-presentation.. is a very strange view that just seems patently at odds with what people mean.