Well, then I'm relieved this isn't a humanities lecture. And that you're not in a position to grade my work.
How it works in the real world is that you don't get to tell people (especially complete strangers) what they think or what they mean. This is widely and correctly viewed as stupid and arrogant. Instead, you can have a conversation with them and learn what they think by listening to the answers to your questions.
You can, of course, explain how something they said came across to you. There will often be disconnects here. And talking about those disconnects can be valuable to both parties. That's one reason why I spend so much time engaging with readers. But given that you are not in the person's head, it's almost always going to be on you to recognise that your interpretation might be inaccurate.
As far as "trans women are women," my take is, and has always been, that trans women are trans women. I've asked countless times, in person and online, and nobody has ever explained why acknowledging this is a problem.
The word "woman" (or its linguistic equivalent) is used by very slightly less than 100% of the world to refer to adult human females. This is true even in countries and cultures that embraced gender-non-conformity millennia before we did in the West. The Kathoey in Thailand are considered distinct from Thai women. The various two-spirit identities in Indigenous cultures are considered extra "genders" distinct from women. The Muxe, the Hijra, the kha’-nun-tha’ triad of the Arabian peninsula, these are all distinct from women in their respective cultures.
This isn't bigotry. It's not transphobia. It's not "biological essentialism." It's just the commonly understood definition of a word. This bizarre campaign to reframe simple, neutral, widely used language as hatred or oppression is truly surreal. And only serves to distract from (and in some cases increase) the actual discrimination that trans people face.
If trans women literally are women, what is transition? What is gender dysphoria? If women can have penises and men can have vaginas, what is the "mismatch" between their bodies and minds that trans people speak about?
Lastly, yes, at least as it's commonly thought of today, being trans is a medical phenomenon. Being trans in 2023 is pretty much synonymous with puberty blockers and hormones and surgery. And while I firmly believe that adults should be free to do whatever they want with their bodies, I think far greater care needs to be taken with children. Care which, again, is very clearly not being taken in many well-documented cases.
And yes, actually, this "huge problem" is being seriously discussed in medical journals and the like.