That is a fair question / approach and sure it is a change but there is no ability to transition sex, nor is there an ability to transition gender.
As gender is simply a societal snapshot of typical behaviour / appearance / etc of the sexes, so a man imitating the female gender simply expands the male gender… that’s why high heels used to be a male footwear, now seen as female / pink used to be the colour for boys, now seen as for girls etc - the perception of what is male / female gender changes as people change what they do - rather than those people somehow becoming or transitioning to the other gender…
so - change, yes - transition, no.
of course change can happen with anyone, and change is not always positive - when people claim to transition’ it is the change which upsets because it is effectively a lie - if a man ‘transitions’ to being a ‘woman’ (in their mind!) then they are effectively saying to their family / friends / wife - either, I have been lying to you up to now, the real me is a man in a dress etc, or they are now living a lie - and in reality, probably a bit of both… It is the forcing others to live that lie, or publicly demonstrating that they have been fooled that can be so upsetting - the man the woman married is not the man she thought, but a different shape of man.
It is no different to suddenly telling the wife that he is not British, an accountant who enjoys football, but a Russian spy who assassinates industrial leaders for a job, those conferences are visits to spy on other countries etc - that person hasn’t transitioned, they are just a different shape of man - but there has been a lie in there and that, alongside the wife being made to look foolish for having been conned is the underlying issue
it is no different to a man who is a normal slightly overweight middle aged chap who suddenly joins a gym, loses 3 stone, starts doing triathlons, every spare moment is for training and evening chat is all about protein mixes and reps on weights etc - the historical friendships are all dropped and new friends come over who sniff and disapprove of anything containing sugar etc - that isn’t transition but it is change…
so, no, people can’t transition in the way the trans community would have you think - it is not possible for a man to ever be anything other than a man - however they can change how they portray as a man and in doing so - they show that others have been fooled / are now being forced to accept something new - and in it all are lies. Especially in this discussion where a part of their change is the expectation that others will support them in their play acting as a woman and agree to also lie
the language is a clever tool - transgender is chosen to imply the image they wish to portray - transition is a soft word to allow a range of stages (it currently even includes those thinking about it which even were it real and you could transition would be nonsense) but it allows a claim to be harder to disprove. Gender is deliberately chosen because it is too easy to prove that sex can’t be changed, whereas gender is a nebulous and fluid concept making it easier to pretend that you can transition
ironically where they overplayed their hand was to push harder on it meaning a factual transition or switch at a sex level by insisting that they were now actual women and that made it easier to disprove!
so, in many ways I agree with you - gender does have a meaning because it says in shorthand that I want to present as the societal stereotype, or that actually you are someone pushing the gender concept of being male and therefore please see me slightly differently, it can be saying that men can also be more sensitive and emotionally attuned rather than the gender stereotype / it might be saying that men can also be carers, nurses, stay-at-home parents, arty etc (and equivalents for women clearly) - but none of that makes them a woman / none of that changes their sex or gender - it simply helps to expand the overall societal understanding of being male / female - and that is a good thing - to not stereotype, to allow boys and girls to play with any toys / do any activities / even wear any colours or clothes… but that is a positive affirmation of difference and acceptance - it is not ‘transition’ which is to narrow down and confirm stereotypes- which restricts what people can do - which is built on lies and deceit