This statement overstates the certainty, but it is not based on a "feeling" as opposed to a "fact".

No, the argument is based in feeling rather then fact.

The WHO is likely to declassify it as a mental disorder in the ICD-11

That's simply just a argument to authority.

evidence suggests that most of the distress transgender people experience as a result of their identity comes from the social rejection, harassment, and violence they're subjected to, not their identity itself.

So why is the rate so significantly higher when compared to Black communities? Were society constantly degrades them as lower class citizens, they face social rejection, harassment, and violence. There are all the same factors, so the results should be the same.

Consider:

Transgenderism Is A Mental Illness, Not A Civil Rights Issue https://archive.is/jcIxp If someone came to a doctor and asked him to cut off a perfectly healthy arm because it just felt “wrong” for the arm to be there, should the doctor do it? This isn't an idle question because this does happen with a mental illness called Body Integrity Identity Disorder (BIID). People who have it feel as if they're not supposed to have a certain body part, like an arm or leg. As a general rule, doctors won't remove a healthy body part; so some of these poor deluded people crush, mangle, burn, or otherwise deliberately destroy their own arms or legs in order to get a surgeon to slice them off. This raises a question: Are surgeons who refuse to remove healthy limbs from people with BIID doing them a service because they're mentally ill or are they denying them their civil rights? MOST of us would say that a surgeon who refuses to cut off a healthy leg is doing the right thing. Of course, not everyone would agree. In fact, there are some people who will tell you that mental illness is a “super power.” Additionally, your mortality rate will be 51% higher than the general population because of suicide and all the female hormones you’ve pumped into your body en masse. In fact, the suicide rate for people who are transgender is 25 times that of the general population according to the American Psychological Association. http://www.eje-online.org/content/164/4/635.full.pdf

Gender Identity Disorder and Schizophrenia: Neurodevelopmental Disorders with Common Causal Mechanisms? https://archive.is/mV9Ic Clinical evidence suggests that schizophrenia occurs in patients with GID at rates higher than in the general population and that patients with GID may have schizophrenia-like personality traits. Conversely, patients with schizophrenia may experience alterations in gender identity and gender role perception. Neurobiological research, including brain imaging and studies of finger length ratio and handedness, suggests that both these disorders are associated with altered cerebral sexual dimorphism and changes in cerebral lateralization. Various mechanisms, such as Toxoplasma infection, reduced levels of brain-derived neurotrophic factor (BDNF), early childhood adversity, and links with autism spectrum disorders, may account for some of this overlap. So people with GID are similar to those who have schizophrenia-like personality traits which suggests that something in the brain is fucked up which can stem from infections, autism, some brain imbalance or childhood problems. A Follow-up Study of Boys with Gender Identity Disorder https://archive.is/Jru5t This study provided information on the long term psychosexual and psychiatric outcomes of 139 boys with gender identity disorder (GID). [...] At follow-up, 17 participants (12.2%) were judged to have persistent gender dysphoria. Regarding sexual orientation, 82 (63.6%) participants were classified as bisexual/ homosexual in fantasy and 51 (47.2%) participants were classified as bisexual/homosexual in behavior. So here they studied boys at around 8 and then at 20 regarding the development of GID. Of these 139 boys which had GID at the first study only 12% had it 12 years later, 47% were bi/gay and 41% were hetero or asexual.

Personality Disorders in Persons with Gender Identity Disorder https://archive.is/PHs9D Persons with GID compared to cisgender heterosexuals have higher presence of PDs, particularly Paranoid PD, avoidant PDs, and comorbid PDs. In addition. MtF persons are characterized by a more severe psychopathological profile. Short: They do have more PDs and MtF are even more damaged then FtM

Psychiatric Comorbidity of Gender Identity Disorders: A Survey Among Dutch Psychiatrists https://archive.is/3Rwrm These respondents reported on 584 patients with cross-gender identification. In 225 patients (39%), gender identity disorder was regarded as the primary diagnosis. For the remaining 359 patients (61%), cross-gender identification was comorbid with other psychiatric disorders. In 270 (75%) of these 359 patients, cross-gender identification was interpreted as an epiphenomenon of other psychiatric illnesses, notably personality, mood, dissociative, and psychotic disorders. In around 75% of the patients, GID was seen as the result of other personality problems / illnesses. Psychiatric Axis I Comorbidities among Patients with Gender Dysphoria https://archive.is/dycBX

Psychiatric Axis I Comorbidities among Patients with Gender Dysphoria https://archive.is/dycBX Eighty-three patients requesting sex reassignment surgery (SRS) were recruited and assessed through the Persian Structured Clinical Interview for DSM-IV Axis I disorders (SCID-I). Results. Fifty-seven (62.7%) patients had at least one psychiatric comorbidity. Major depressive disorder (33.7%), specific phobia (20.5%), and adjustment disorder (15.7%) were the three most prevalent disorders.

The rate of successful suicide is extremely correlative with conditions of mental illness. See http://depts.washington.edu/mhreport/facts_suicide.php

And

There's also quite a bit of evidence showing that transgender people are more likely to attempt suicide if they experience social rejection at home, work, or school, suggesting again that the problem is primarily the result of how they're treated. See this survey, for example.

Obviously, that's intuitive. People who face social rejection are always going to have higher rates of suicide that those who do not. Look, I don't think there is anything morally wrong with being trans, but its simply inconsistent to not call it a mental illness. Someone biologically is either a Man, Women, or intersex. In example, I can think I am a dinosaur, get scales grafted onto my skin, inject dangerous medication to make me feel more like a dinosaur, but I cannot become a different species. I am a human, even if I 100% identify with being a dinosaur I just can't become one, and god damm I wish I could. I really think trans people should seek help, I honestly do not wish them any harm. Our society stigmatizes them, and that's a major problem we need to overcome. It's not about rejection, its not about weather its right or not, but to say that a group with nearly 20 times the suicide rate when compared to the average does not have a mental illness is just ridiculous.