To say that it’s not possible to convince someone they’re trans contradicts direct testimony by detransitioners, stats.
You’re not paying close enough attention to the social contagion taking place and being described online amongst tweens and teenagers.
Nor to the hamstringing of therapists who cannot probe why a child believes their trans, because that’s considered conversion therapy.
For some children, the idea that they were born in the wrong body is being offered up, or being grasped at, as the one-size-fits-all reason for their distress — when that distress may well instead be caused by abuse, fear of their own homosexuality, all sorts of issues within the family or school, etc.
There is something called iatrogenesis. In the 80s, it led to many mental health patients being diagnosed with multi-personality disorder. For several years, specialized inpatient MPD clinics opened and MPD therapists made a LOT of money of those so diagnosed. And several people claiming MPD diagnosis became famous, in those days before the internet, on talk shows and magazines.
Now, today, that condition is called Dissociative Identity Disorder and recognized as being extremely rare, and therapists are taught that it’s something that can be iatrogenically induced if they’re not careful in treating patients with certain issues.
If MPD can be iatrogenically induced, then yes absolutely gender identity issues, a sense of oneself in “the wrong body” can be.
And children really really want to please the adults in their lives. That’s what makes them so vulnerable.