However, it seems clear that you are attempting to follow a Socratic method in engaging in an argument for Biological essentialism. Here is an example of how to accomplish your goal in a form that is more functional to a comment thread than point by point posting.
1) Humans develop from a single cell egg to a complex multicellular organism.
2) The form of human includes various cellular expressions that create organs, tissues, etc. that provide specific functions for survivability and perpetuation of the species, which are universal across the species in general, though may differ in some way individually.
3) One outcome in development from the egg is sexual dimorphism, when the developing fetus's cells organize into a pattern that is labelled male or female, also known as sex differentiation. This differentiation continues at various stages throughout an individual's life.
4) Sex differentiation not only refers to the physical development of the observable body, but also requires that the brain physically in preparation to manage the biological needs (endocrine) for the developing sex and to process sensory input for the body.
5) Development from a single cell to a complex human is far from a perfect process, as evidenced by the variations that are completely benign to those that result in the death of the developing fetus.
6) Variations in the developmental process do result in incomplete or even mismatched sex characteristics that would have been assumed by karyotyping (which is rarely done).
7) Since evidence is easy to obtain showing variation in the sex based development of physical bodies, and evidence also shows variation in development in physical brains, it is not without reason to expect the potential of a variation where the brain develops according to the needs of one sex and the body develops the opposite.
8) Current research is mounting evidence for #7.
So if 7 is true, how would we expect this to manifest from observable behavior?
1) Given that we are culturally reinforced with expected gender norms that encourage some means of expressing one's sex through gender expression (think clothes, behaviors/mannerism, occupational choices, etc.) our cultural understanding of sex is limited by our vocabulary of gender and how we perceive it in others.
2) Instinctively, infants have a drive to mimic behavior that they observe, thus enabling them to learn. However, children demonstrate a preference for mimicking behavior that they identify with. This is where many children start learning gender roles as expressed in their culture.
3) Those whose brain sex matches their body sex have no trouble meeting societal expectations, nor conceive of any issue concerning their own anatomy.
4) Those whose brain sex does not match their body sex have no frame of reference to describe it. Early attempts to mimic the behaviors of the identified sex are likely met with punishment/shaming. For most, this shuts them down and they learn to hide their issue. With no means to discuss what they cannot describe, they reach for the next closest thing, which is the symbol of their desired sex as expressed by those in the opposite gender. Clothes, behavior, etc. become symbolic to the point of becoming the only language available to express/explore their inner identity.
5) worse are those whose brain did not develop completely male or female and they are stuck in some artificial limbo dictated by societal gender norms. Regardless, such people are still human beings, no less than any other. Many wish peace with the conflicts they experience internally. Many have also had to hide because they cannot articulate or communicate their pain in a way that our culture finds meaningful. Some succumb to the pain and take their life.
In the end, whether you believe that transgender is a real physical condition or something simply "in one's head", it does not matter. There is no excuse for denying an individual their humanity or to dismiss them as an "other". Furthermore, look at your view points now and ask yourself, if this is proved to be something physical and "real", what have you accomplished? On the flip side, if it is proved to me to be purely behavioral/cognitive (ie. not physically interlinked from a developmental standpoint), then at least my actions were done with in keeping with the current science and medicine available and my view points subject to reinterpretation based on new evidence.