hank you for your email.
The government is aware that there is a conflation of sex (male or female) and gender (boy/man or girl/woman) in law and almost everywhere else because often when a person is asked how they identify, they reply 'male' or 'female which are, of course, descriptions of sex characteristics, and not the same thing as identifying as a man or a woman. In the cisgender population, such a conflation is not always problematic, but in the trans/non-binary population it is unhelpful.
There are common assumptions made at birth. It is assumed that sex characteristics, and gender identities are inevitably binary, when in fact we know that there is everything in between; it is also assumed that genital appearance determines the gender identity. Although, typically, sex and gender will be congruent, this is not inevitable. Also, gender identity is not the same thing as gender expression although, usually, of course, we anticipate that gender expression will reflect gender identity. So, typically, male genitalia will be associated with the psychosocial identification as a boy, and a gender expression that is largely regarded as masculine; and vice versa.
You have made the sex/gender conflation when you contradict the point that “it’s your brain that tells you you’re a boy or a girl”, and continue with "surely it’s their genitals that tell them what sex they are? Yes, the genitals indicate sex or, at least the sex you can see, but, as above, that is not an infallible indicator of a person's psychosocial understanding of themselves as a boy or girl (or non-binary). It's the brain, not the genitalia that tells you if you are a boy or a girl, or non-binary. Gender identity depends on how the brain is configured. Of course there are male and female aspects to all brains, although overall brains are more alike than unalike, but there are differences in anatomy and function which impact on gender identity and these differences are found in trans people. Often they are associated with unusual hormone levels prenatally.
We learnt these lessons many years ago, when it became apparent that surgeries on infants, born with ambiguous genitalia, to create a female appearance, do not guarantee that the child, no matter how assiduously raised as a girl, would identify as such. Therefore something else had to be going on. The gender identity was not necessarily a match with the female appearance and the gender of rearing. This practice is now unlawful in some jurisdictions.
There is peer-reviewed scientific evidence indicating differences in the brains of those whose identity is not congruent with their sex as registered at birth (hence the new terminology 'gender incongruence'). It is on the basis of 'current scientific evidence' that the WHO has now reclassified 'transsexualism' by moving it out of Mental and Behavioural Disorders. So, it is no longer regarded as psychopathological but somatic. The same journey was made by sexual orientation in 1992, when the WHO dropped it. A person's sexual orientation is not a choice, and that is generally accepted now. Nor is a person's gender identity a matter of choice. We are not all born cisgender and straight.
The most recent review of the "biological correlations in the development of gender dysphoria" is in The Lancet 2016 June. (Dysphoria is the discomfort associated with the 'incongruence').
Experimentation with gender expression whether temporary or permanent, may or may not indicate that a person is transgender. It is how they describe themselves - the person they know themselves to be, that is the key. Many women wear quite masculine clothing, at least some of the time, but they still regard themselves as women. A person assigned male at birth who does not identify as a man, will experience extreme discomfort, will ultimately be obliged to transition, to bring their gender expression, name, pronouns and sometimes, sex characteristics in line with their identity, so that their social interactions become appropriate. The same is true of those assigned female who identify as boys.
Assuming that experiencing gender dysphoria is merely a matter of wearing clothes that are more typical of the opposite gender is to trivialise what is a real and even life-threatening condition, if the identity is not affirmed and supported socially. You can be comfortable or uncomfortable within your social construct, but the construct itself does not make you who you are. Erring on the side of caution means supporting a young person who says that their identity doesn't match their assigned sex. Failure to affirm their identity can lead to serious mental health issue.
I hope this helps. it's really only skimming over the surface