1. Sexual dimorphism is prominent enough that it can be identified in skeletons even after all other cells have rotted away.
2. Every cell in the body has DNA and a sex chromosome. This is necessary because the 2 sexes code for very different endocrine systems (your hormonal systems), which are crucial regulators of all other organ systems. Your skin, heart, lungs, muscles, digestive system, and (of course) reproductive system are all regulated by your endocrine system.
3. All intersex conditions cause variations of male or female sex characteristics. Some people occasionally have both male and female parts, but no one who experiences that is a true hermaphrodite, because the endocrine system only allows one to operate functionally (if either system Does operate, which is not always the case). There is no third type of genitalia or endocrine system associated with intersex disorders. When a person is born with just one chromosome, it is always an x chromosome. It results in atypical female development, not a third sexual state. Thus, transitioning to any nonbinary state is impossible. There is no naturally occurring nonbinary or gender fluid person, the existence of these genders are a social construct made to describe certain personalities.
4. While there are variations in the arrangement of grey matter in the brain, no research has proved that this has to do with sex or self-identified gender. These differences likely has to do with the brains plasticity and responses to environmental stimuli that influence its development. Furthermore, if brain sex was real and could be tested to identify transgender people, ALL people seeking trans healthcare would be required to have brain scans as part of the diagnostic criteria. That does not happen; you can ask your transitioning friends or read interviews of detransitioners.
6. Puberty blockers, HRT, and affirming surgeries all have potentially life-threatening complications associated with them. Despite what the doctors on Ted talk may tell you, puberty blockers like lupron are not safe, they are associated with early onset bone degeneration. Testosterone applied to a female body is associated with an increased risk of post-menopausal health issues like vaginal atrophy. This issue may be mild on its own, but it increases your risk of BV, which is likely what led to Buck Angel nearly dying of sepsis based in his own account of the situation.
These are not healthy reactions to HRT. these are signs of sickness and pain caused by attempting to force incorrect hormone regulations onto cells programmed for a specific set of hormones. I will not describe the complications associated with surgery because when trans surgery goes wrong, it is often very painful and traumatizing for the victims. However, i do think the high rates of complications for all gender affirming surgeries is indicative that it is not actually possible to change your sex. If you wish to learn about how a person's body may reject "gender affirming" surgeries, Please go hear stories of complications directly from trans people because I cannot describe those experiences in a respectful way.
Scientifically, it's just not possible to change your sex. So what about gender? What is gender? It's not your physical body. It's not the structure or function of your brain. When you analyze gender, at the core, it is a feeling. It's an emotion you have. Like any emotion, it is volatile (subject to change -> explains why many people question their identity frequently before and after coming out; explains genderfluid identities; explains detransition). Like any emotion, it is a reaction to your environment.
Many trans people have stressful home environments. Many trans people are victims of CSA or rape. Many young trans people are autistic, and have never been able to fit in with others or correctly follow social rules like gender roles (and if you've ever lived around other people, been to school, been to work, or been outside, then you have been subjected to gender roles, whether you realize it or not). Many trans people are also gay or bi, and may have grown up in an unaccepting community. All of these experiences cause feelings of alienation, feelings of being "wrong" or "abnormal," and detachment from your body. Gender is a way to explain and justify those feelings, because it is easier to change yourself than it is to change an unaccepting community.