Sorry to keep going back to 'what a woman is' but it does seem incredibly important to you, @AlphaTransWoman , and obviously as you advocate for basing law and policies around this definition it's important to us.
Feel free to go through and pick up where I have gotten you wrong.
Can I see if I have understood your claim:
You acknowledge (I think) that there are male and female bodies. You believe there is an incredibly strong, almost one-to-one correlation, throughout all of humanity with having a female body and having some sort of checklist of psychological traits (and with a male body and 'male mind' traits). You have also referred to "the way they feel about themselves and wish to live" without giving any more information on what this actually means.
You haven't said on what data you have concluded this, or even given a list of these traits other than "men are more competitive and rational" and "like to be assertive and in charge of things", and women are more "cooperative, empathic and emotional, more likely to to be kind and take a supporting role" - or said how you would measure them, or what it means if someone's ability/personality changes over time, or what even it means to 'be emotional'.
Let's say you think female people are 'above average' on these traits and there is therefore a distinct gap between how male people do on these and how female people do (so you wouldn't really see any overlap, because you claim that the traits are what distinguishes a 'male mind' or 'female mind'.)
You acknowledge there are 'some outliers' - males and females whose mind doesn't 'match' your list of traits. How many, we cannot know, but presumably millions worldwide.
Those with 'woman mind' traits are women, and this includes male people with those traits.
Those with 'man mind traits' are men, and this includes female people.
The fact that millions of female people can have 'man minds' does not suggest to you that in fact psychological traits can present equally in both sexes, but you conclude instead that their bodies are the wrong sex for their mind.
Based on this alone, you believe that 'man mind' people should be treated as male in all situations bar a very few, and same for women minds being treated as female. Bear in mind you say as a woman you are less rational than 50% of the population yet think it is fine to advocate for both sexes on this.
You think that the female body is a visual cue that the person has 'woman traits' and so appearing as a female, or taking on some female physical or social factors like she/her pronouns, female names, gendered clothing etc, tells society that 'this person has a woman mind and must be treated as such', hence your linking of appearance and psychological traits.
Is this more or less accurate?