In my long experience someone can be as brave and stoic as all get out but it would not cut it with the "You're not a man" crowd if he has the wrong voice, mannerisms, interests etc.
On the other hand if someone has the right mannerisms, voice etc he will be accepted as a man no matter how cowardly or unstoic he is.
So we have, on the one hand, biological males who consider themselves "men" in some mysterious non-biological sense.
And on the other hand we have biological females who consider themselves "men" in some mysterious non-biological sense.
I don't understand either, but I don't see any big difference, never mind an extreme difference.
I think we are dealing with three different senses of the word.
When in doubt, we should ask google. Google knows everything.
When I google the phrase "real man", the first hit was to Urban Dictionary. In that lingo, a "real man" was synonymous with "old fashioned" in the way they act toward women.
The next entry was a question "What does it mean to be a real man?" And the answer began,
" 'A real Man' for me, personally is someone with true Dignity, Integrity, and willing to sacrifice himself to take care of others.'A real Man' is someone who has the up most respect for Women, therefore does not harm them in any way.'A real Man' is someone who doesn't give up as easily..."
That was the sense I was talking about as a "real man", and it seems that me and google are on the same page with that phrase.
What you are talking about is someone who has effeminate mannerisms, and
certainly their masculinity is questioned, and, especially in times gone by they were ridiculed, shunned, or bullied.
Similarly, and with some overlap, a homosexual might be considered less masculine.
So those are three different senses in which someone's "manhood" might be thrown into doubt. However, in none of those senses would anyone think to call those people actual women.
Interestingly, we can think of the corresponding cases for women.
"Real woman" is somewhat fuzzier, and used far less frequently as a phrase than "real man". Googling the phrase ends up with far more diverse answers. Interestingly, the most common use of the phrase in the top google hits was actually some sort of "less than perfect" sense. "Real women" were ordinary women who were not supermodels or did not fit some sort of idealized version of beauty or sex appeal. However, there were also other uses of the phrase for all sorts of different attributes. The phrase wasn't as common or the usage not as consistent as "real man".
On the other hand, corresponding to the sense of effeminacy in men, women who are "butch" might be called less feminine, and homosexual women might have their femininity questioned.
Again, though, though, these sorts of women would not be considered actual men. People who were not "real men", or men who were "girly" or women who were "butch" weren't perceived as the opposite sex. They were more perceived as somehow sexless.
So there are multiple senses of words that might be used, or have been used in the recent past, to signal that a person who was a given biological sex somehow did not fit into some sort of idealized version of that sex, and so were not "really" a man or a woman, or were "less of" a man or woman, but in no sense of those words was there ever a sense that made them actually part of the other sex.
In short, I'm still not following your reasoning. If we talk about biological males who were somehow said to not be "real men", or otherwise characterized as something other than male, they sure as heck weren't considered to be "real women" either.