This argument makes two basic assumptions:
1) There is no metaphysical trait that is unique to either sex (the only differences between the sexes are physical).
2) As a society, we strive for the sexes to be as equal as possible.
Now, if those two assumptions are true, then it is a simple matter to prove that separating the terms “gender” and “sex” is without merit.
I ask the question, how can someone “feel” more a man than a woman, or vice versa?
When I ask that question, usually it is responded with the assertion that the individual has more masculine or feminine traits.
What is a masculine trait? What is a feminine trait?
I posit that there is no such thing outside of biology.
Usually activities or metaphysical traits are associated culturally as masculine or feminine.
For example, caring for children is a feminine trait. Does that mean that caring for children makes you a woman? No, men can care for children just as much.
Aggression is considered a masculine trait. Does that mean an aggressive female is a man? No, as women can be aggressive too.
Is there any trait, not rooted in biology, unique to one sex? Can only women dance, and only men fix cars?
No, such ideology us outdated. Women can do whatever a man can do, and vice versa, assuming they are physically capable.
Therefore, the logical conclusion is that it is impossible to discern whether you are a man or a woman other than through physical means, as men and women are identical other than their physical bodies.
If it is impossible to determine one’s gender other than through physical means, then the term becomes no different than “sex”.
If we, as a society, decide that if you have more culturally-defined masculine than feminine traits you are a man, regardless of sex, then that enshrines cultural norms and gender stereotypes as a pillar of our culture. This would effectively mean that, as an example, only men can be mechanics, regardless of sex. The distinction of sex and gender inherently relies on the existence of societal gender norms/stereotypes.
Such a culture borders on absurdity, and is not one to strive for.
If we, as a society, decide that gender and sex are one and the same, then we acknowledge that men and women are equal in opportunity. Specifically, that one’s interests are not defined by their sex/gender, but by the individual. This would lead to the eventual abolition of gender norms.
*As an aside, this is applicable to transsexual individuals, but not those who suffer from sexual dysphoria. Sexual dysphoria is characterized by an extreme rejection/aversion to one’s own body. The only known treatment for sexual dysphoria is sex-reassignment surgery. If left untreated, it is likely the patient will either mutilate themselves or commit suicide. This differs from transsexual individuals as being transsexual is not a mental illness, and is characterized by a rejection of how they are perceived by others. Transsexuals are not inherently uncomfortable in their body, which makes them fundamentally distinct from those suffering from Sexual Dysphoria. However, those suffering from Sexual Dysphoria will usually be transsexual as well. This boils down to not all transsexuals have sexual dysphoria, while all those with sexual dysphoria are trans.