On what basis do professionals who recognize gender dysphoria support risky and permanent medical intervention for those seeking gender re-assignment? Before I pose my question, here are some statements from a slideshow on &quot;Understanding Gender Nonconformity in Childhood and Adolescence&quot; by Robert Garofalo, attributed to the Children's Hospital of Chicago, and hosted by the American Academy of Pediatrics (AAP). They officially support affirming gender change in children, however there is a group of pediatricians who actively reject that position.
According to this slideshow, gender is a social construct (page 7), which &quot;[v]aries by place, time period&quot; .
Next I'd like to list the slideshow's listed side effects and irreversible effects of hormone therapy. Pages 39-41 show the side effects of testosterone therapy.

Irreversible Effect of Testosterone Therapy

Lower voice pitch
Increased hair growth (arms, legs, chest, ab)
Mustache/beard growth
Male pattern hair loss (temples, crown) and possibly baldness
Genital Changes
Genital changes (clitoral
growth and vaginal
dryness/fragility)
Fertility?

Side Effects/Risks: Testosterone

Increased cardiovascular risk

Increased weight
Decreased HDL, Increased Triglycerides
Increased BP


Increased insulin resistance
Hepatotoxicity
Mood changes: irritability, aggression
Headaches
Acne
Polycythemia
Theoretical risk: breast/endometrial cancer


Given these side effects, on what medical basis do health professional support this?
If a person doesn't like themselves they get help with their self-value.  They learn the valuable things about their unique identity and also identify why they began to devalue themselves and deal with those root issues. People with phobia's are taught to manage and improve their phobia, not embrace it.
My point is not to compare one disorder to another, but to show that regardless of the type of disorder that the standard treatment is not acceptance, but rather to reveal deeper issues and otherwise manage and overcome the disorder.
Gender Dysphoria is treated categorically different, but there has been no new category defined on which to base that decision.
I know this is a sensitive topic and has many personal stories, but I'd like to focus on the professional medical position and reasoning for that position.
I hope I am qualified to answer this question. I am not a psychologist but have worked with transgender persons in volunteering positions a number of times and am fairly well researched on the topic.

The biggest key point as I have studied simply is based on health outcomes as opposed to comparing this to mental illness.

This page talks about the practical health outcomes of the treatments. Individuals who identify as transgender already often suffer from a variety of issues that reduce both their quality of life and in some cases health. These can include developing mental disorders if they do not get treatment and even self harm or suicide. Overall most of the linked studies in that article showed that the benefits largely outweighed the risks in an overall health decision.

Now you imply that other treatments are used for most conditions which have effects on mental health, usually either "talking cures" or medications. The difference being in almost all cases these treatments are ineffective or even make the situation worse in transgender individuals. 

I cannot find a study to link to this which is publicly available right now but in short, treating transgender individuals with treatments used for mental illness usually makes the condition worse. In many cases it causes additional depressive disorders to form as well as long term self image problems and self hatred, as well as increasing the risks of self harm or suicide.

So in summary, it is not to say the treatments used for transgender persons are risk free, but merely that they are better than the alternatives both of doing nothing and of trying to use a purely psychiatric method to treat. As both of those tend to make the condition gradually worse and no other treatments are known which produce a consistent improvement.