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Transgendered people obviously exist and they are not suffering from any mental issues...
They are not NECESSARILY suffering from any mental issues.
Gender dysphoria is still considered to be a mental health issue if it causes the individual significant distress. It is still a mental health diagnosis in DSM-5. It is considered a condition, rather than a disorder. But dysphoria absolutely CAN be a mental health issue.
In fact, the distress of dysphoria is the claimed reason for why transgender people NEED medical intervention. They argument is that without cross-sex hormones, without surgery, they suffer significant mental distress, and therefore those treatments are medically necessary in order to treat their diagnosis of gender dysphoria.
If there were no mental health issue, then there would be no need for medical or pharmaceutical intervention. Of course, any individual can obtain those interventions as
cosmetic procedures. But not as
medical procedures.
Additionally, it is worth noting that Autogynephilia continues to be considered a disorder. It remains a diagnoses under the Transvestic Fetishism grouping of Sexual Paraphilias in the DSM-5. While not all transgender identified people have autogynephilia, some do. Some have been quite open about their own diagnosis.
So off the top, it's false to make the assertion that no transgender people are suffering from mental issues that are directly related to their identities as transgender. Perhaps some are not, but a great many make the claim that they are suffering under severe gender dysphoria in order to justify medical intervention.
Beyond that, a very large number of people who identify as transgender have other mental health issues. Autism and ADHD are significantly overrepresented among transgender identified people. There is also a disproportionate incidence of anxiety disorders, bipolar disorders, and eating disorders. There's a very high rate of pre-existing self-harm disorders in adolescents who identify as transgender.
If we cannot acknowledge the reality of the mental health aspect involved in this topic, we will never be able to provide appropriate and compassionate care.