No, I said “gender role” in quotes for a reason — to group it together as a concept. If you want I can rephrase it to “societal role historically associated with a particular set of physical traits”, but I thought that was apparent.
The argument isn’t that sex and gender are entirely unrelated concepts. Just that they’re not inherently equivalent.
You still haven’t said what gender is, in the sense of an inherent, permanent property that allows one to coherently say “I was born in the wrong body.” We all know what gender roles are.
My understanding, and I’m not a professional here, is that child development studies indicate that children develop a sense of gender identity by about age three. There’s a lot of debate about how this gets determined — whether it’s biological or cultural or both. This is, as you might imagine, very difficult to ethically experiment with. After this age it’s then also very difficult to change that gender identity, such that it’s legitimately easier to treat a sex/gender mixup by helping the person involved adjust their gender presentation to match their internal sense of their gender.
You’d be free to argue that this isn’t an inherent property, I suppose, given initial probable-fluidity. But since it seems to settle into being a largely fixed part of your psyche before the point you’re likely to have permanent memories, I’m inclined to view that as a meaningless difference.
It’s at about the same level as arguing whether sexuality is an inherent property, I think? It’s another of those “it might be hardcoded or it might be early-development cultural, but it’s basically impossible to change it so…” things.
As I said before, "born in the wrong body" is actually not quite accurate, but it's used to approximate an explanation for people who aren't familiar with ideas like gender roles. Gender isn't a biological concept, it's a sociological one. Gender identity is whether you identify with the gender roles of male, or female, or neither. I didn't mean to imply that it being an "internal property" meant it was biological, as I've been trying to explain - it's psychosocial.
Edit: I think fundamentally, if you don't object to treating trans people decently like using their preferred pronouns and name, or getting surgery, I don't think it matters too much. I'm not an expert on the definitions by any means, my primary concern is opposing justifications to mistreat trans people, so if it's just a matter of terminology I guess my only suggestion is to read into what the relevant fields of study have to say if it's something you want clarity on.
