Whether trans is an insult depends on how you use it. The way you are using trans changes the implied meaning of trans to something trans people are keyed to implicitly notice - whether it's being used as a null category.

A lot can be derived from language from relationships. If you have man and trans man you create a non-category. A "not man" a "fake man" if you have cis man and trans man it is an acknowledgement that these are different states of being a man that acknowledges the difference of experience but places the emphasis on manhood and similarity to other men rather than the differences. "Biological man" and "trans man" becomes again man and "disqualified by biology man". If I am not a "biological man" will you also try and imply I as a trans man am a "biological woman"? Even if I haven't transitioned at all that's taking everything I hate about my day to day existence and shoving my face in it.

Also

I wouldn't worry about men slipping the noose by pretending to be trans women. If you look at penal systems they basically all conform to a similar model at present. Like the US loves to incarcerate people and last I checked, pre Trump, of the places that actually tracked the number of trans women the count of how many trans women were in women's prisons was 17 compared to the over 500 in mens prisons. These women may be post op meaning they have neither testes or penetrative organs and they may have been on horomones so long that their bone density, nerve structure and muscle to fat ratio is more in common with a cis woman but there's no actual guideline for trans people about when they are deserving of the same protections as cis women when in prison. Ending up in a mens prison as a trans woman means rape and assault is basically part of the deal. Furthermore when gender affirming medicine is deemed a luxury in such situations and removed these women don't have any naturally created Horomones anymore so they effectively go through menopause and osteoporosis at a young age because "it's outrageous that we should pay for gender affirming care!". You might have committed the same crime as the people around you but if you're trans you are doing harder time...because people assume you're a man or at least not woman enough. Hardly seems like justice where I am standing.

Sports have a similar issue. What is sport for exactly? It can't all be reaching some kind of physical pinnacle based off arbitrary distinctions of body ratios and hormone levels after all -the Paralympic games exist where different but at least kind of similar disabilities are matched together.

There are way more options in sport as a person with a disability than as a trans person these days. If you are looking at sport from the perspective of a social activity with community attached working towards mutual excellence or as access to pastimes that encourage healthy levels of activity then there's a massive impediment to access because even things where sexual phenotype doesn't matter , like sport fishing for instance only, allows trans people to compete in their birth sex category if at all. This segregation forces athletes into single sex spaces that are proven to be psychologically damaging to them defeating any benefits from the activity. There isn't really a society wide call to make categories that are inclusive co-ed spaces... they are only saying "we don't want you anywhere". It's simply not looked at as a civil rights access to the variety of life issue but a matter of who wins. If a trans woman places 5th in a women's sport category the question isn't, how well she was integrated in that community and whether her win/loss ratio was within comparable margins of the cis athletes in her cohort - its that trans people don't belong there ever.

This framework of relegating a group to the trash bucket based on non categories doesn't look at trans people as individuals with different physicalities and personalities and inclinations. It doesn't weigh trans people on a case by case basis - it flattens them into these cut outs where they are always outsiders and never deserving of empathy or consideration because they automatically represent the worst potential aspect of their birth sex. Getting smacked with misandry and misogyny in turns depending on whatever seems the most situationally appropriate to exclude them.

It also doesn't help that transness is still sort of a cultural failure state and is often internalized by ourselves that way. Oftentimes by the time a trans woman comes out for the first time she's already in a pit. She already bet the farm on trying to be the best man she could be to fix what ails and it did nothing but drain her of her will to live and she has to accept that being a woman is the only conditions under which she can live because she can already seen the finish line where continuing as is will kill her from where she's standing. She's often put off the transition as long as she can and is treading water and minutes from giving up and drowning . So yes. She's a woman from the moment she says in part because that could be the moment of greatest crisis.