I don't understand the discourse that says "you're only /actually/ trans if your sense of your gender isn't affected by how people treat you" because gender is social. No one is born with a gender; we (society) assign gender to babies and when it grows up it will either accept or reject this assignment. No one's sense of gender is unaffected by society and social relations. I'm not gonna (for example) contradict some cis guy's gender like "you only consider yourself a man because masculinity was imposed upon you from birth. If it weren't you wouldn't have formed a male gender identity", I'm gonna have some good faith that he's done the introspection that I'm in no position to do for him.
We cannot really say that gender is entirely social. Gender roles on the other hand, are entirely social. Things like clothes, how we are "supposed to behave", what we are supposed to like, can all be viewed as completely arbritrary, and therefore, as a construct. And the "assignment of gender to babies" are more like imposing expectations of gender based on genitalia.
Gender also has a biological and psicological aspect. It is extremely hard to properly convey to a cis person, as trans, how it actually is to feel unconfortable with your body. Something like it doesn't match. This manga shows it very clearly with the table scene. You can see gender dysphoria being manifested towards the primary and secondary sexual characteristics. But it goes way deeper than that. There is also, yes, the social aspect, but they are only a part of the whole problem.
I hope I could clarify a bit on what you don't understand.
