Gender Theory, from what I can understand, finds it’s defense in social construct theory. Social construct theory is a denial of substance theory which is the basis of the doctrine of transubstantiation. Basically, arguments tend to break down because one side sees ALL reality as a social construct. There ARE NO true substances, just words artificially create the mental conception that this thing is different from that thing.
Indeed, it’s influenced by Buddhist philosophy which is about growing emotionally distant from a situation by recognizing that on some level, nothing is real, that even the “self” is an illusion. As such, we can socially construct “gender” to be whatever we want it to mean.
Whereas in substance theory, we say things actually exist. This is a chair (the substance). All its attributes are distinct from the substance of it being a chair. As such, when a man claims “I am a woman”, we would ask, “What is a woman?” in order to define the substance of womanhood. Generally, we say that womanhood is simply being female, and femininity is the nature of being female. Thus any socially constructed stereotypes or roles for a woman are not authentically a part of her femininity. Only those attributes which come directly from her nature are a part of her femininity.
This gets into the belief that that the sexual differences ONLY relate primarily to procreation, and that all other traits associated with femininity are social constructs. Thus if a man feels he relates to the social construct of a woman more, he can define his gender as being a woman. If an man feels not quite fully masculine and not quite fully feminine (basing it all on stereotypes of what these things mean), then he’s genderqueer and he can dictate to you which pronouns you use for him.
But because they’re arguing gender is a social construct, they are arguing that gender doesn’t exist at all. And because those of us who believe in substance theory are looking for concrete non-socially constructed definitions, they appear to argue their opposite.
My advice to you, then, is to find books on substance theory and social construct theory. You’ll do best just explaining where the conversation breaks down than actually arguing your point.
