not offended by what is said - and yes, polite debate is great... however I think there are some flaws in what you are saying which need to be discussed more because it is only as we unpick the flaws to fund truth that we move to a better society which is more tolerant of all people...
I have to respectfully disagree with the OP, I would not have said 'no they're a man'
I may have clarified when they were born they were a boy, but we all parent differently.
However - this implies that you accept them now as a woman - at the core of current transgender issues is the scientific fact that no one born male can ever be female - the whole of one 'side' bases all their arguments on trying to obfuscate this fact and pretend it doesn't exist - the other 'side' is focused on peeling back those layers of misinformation and deceit to focus on truth...
If they were born a boy then they are now a man - there is no room for alternatives nothing else is possible - so the OP was right to teach her son truth - the person in question is a man. To parent differently from that is of course your prerogative, but I find it hard to understand how any parenting could offer an alternative reason while still teaching truth.
I wouldn't want my child mis-gendering a trans person because I had.
There is no such thing as mis-gendering, this is another fallacy propagated by those who have ulterior motives in trying to persuade the world that there is this magical feely gender thing which if you feel one way makes you male and another makes you female...
this is the Oxford English Dictionary definition of Gender:
'The state of being male or female as expressed by social or cultural distinctions and differences'
i.e. it is about symbolism and stereotypes - it is as society / culture sees it currently - that high heels were originally male footwear and are now female footwear is one good example of how those symbols change perception over time - so gender is fluid and societal - never static and biological... as such a person who wears a skirt today and a tie tomorrow would be demonstrating adhesion to female then male gender - neither would make them male or female.
As gender is fluid and transient - you are not a gender - you simply act or dress or respond in a way seen by society as typical of a gender... Because it is not something that you are, you can not be mis-gendered.
(NB - definition 2 of gender is: 'To copulate. Frequently with with[sic]. Obsolete.' now that does lead to some interesting reflections on the 'trans-gender' movement 😁)
Trans people are born in one gender and live and identify as another...
As per above - sorry, but this is not thought through and makes no sense... unless you simply mean that a baby boy is placed in a blue romper suit but then wears pink shirts as a man?! As gender (see official definition above) is simply a societal shorthand, no baby or young child has any sense of gender identity - they can't because at that age they do not understand society - to be fair, children learn about gender early on as they start to realise that society sells some toys to boys and some to girls, that life is less fair for the female sex, that some jobs are seen as for one or the other etc. - but that has nothing to do with being born or changing...
It's assumed we're cis gender until we're not.
I understand what you are trying to say, but this is understandably offensive to many - the word cis was developed by those in the transgender movement to self-validate their claims that they had changed from man to woman - by calling all those who were born women 'cis-women' they can claim that cis-women and transgender-women are simply two subsections of women - ergo they are women...
I am sure that on reflection you can see how offensive that must be to those born women who need no classification other than female / woman and who object strongly to being 'sub-classified' to allow men to pretend that they are women.
Also, as above gender is something that is a shorthand for how someone appears / behaves in society at that point - you are not 'a gender' - if all men start wearing trousers one leg green and one red, and all women start wearing a blue glove on one hand and a brown one on the other - then by tradition building these would become gender identities
gender has zero to do with sex and let's be clear the underlying discussion here is about sex not gender - no-one sensible cares if a chap wishes to wear a skirt - but pretending that he is a woman just opens up so many issues and as we all know (including those who pretend otherwise) a man can never be a woman...