Okay, I'll play.
In their circles, sex exclusively refers to someones biological sex, and gender is ridiculed as an indefinable concept as vague and - it is implied - as unscientific, as souls (a suggestion that trans people are not and cannot be real. That we are either liars, or deluded). In a world where “sex” and “gender” are used interchangeably by the general public, they use this general ignorance to drum up support for their cause.
The concept of gender IS vague and unscientific, as it is based on societal (more often than not, sexist) stereotypes which vary from culture to culture and can change over time. Not obeying societal expectations of gender in choices of clothing, hobbies, name and presentation can be difficult in a sexist and conformist society, but it doesn't magically turn a male (small gamete producer) into a female (large gamete producer).
In Jay's mind, what exactly IS gender dysphoria? Is it a distressing condition causing sufferers to unfailingly attempt suicide unless they permanently alter their healthy sexed body to relieve it? Or is it a normal state of mind? Why does one person have gender dysphoria and another does not? How does it come about, and why should we not investigate possible environmental causes of it, seeing as it we are told it requires significant pharmaceutical and surgical interventions and social engineering to manage? Why should we take the subjective feelings of the sufferer as empirical truth? By that logic, we should be affirming the beliefs of anorexics that they should lose more weight and paranoid schizophrenics that the voices are real.
By the Goddess, this guy is a fucking numpty.