To impose explanations on other people's experience that contradict how those people understand their own experience is almost always dangerous and wrong headed. This is by no means something unique to this topic- it's a general principle of significant importance.
Don't agree. There are many people who interpret their own experience and look at the world in ways that are totally at variance with the facts.
In some cases this is the result of mental illness - e.g. people with schizophrenia who hear voices or develop the fixed belief that they are Napoleon; people with eating disorders whose body image is disordered; people with body dysmorphia who become convinced that a part of their body is huge and disfigured, when everyone else can see that it's perfectly normal, or who believe that (say) their left leg is not really theirs and should be cut off. People in this position need help from appropriately trained and experienced mental health practitioners. What they don't need is other people agreeing with them.
There are others who develop a fixed belief for reasons that are very difficult to understand, but may be wish fulfilment and/or limited intelligence (emotional or otherwise) - e.g. the world is flat; identifying as a member of a different ethnic group or as a much younger person or a furry. They are free to believe and roleplay whatever they like but they can't force the rest of us to go along with it.
Part of growing up healthy in mind as well as body is learning to know and accept reality, no matter how horrible it is. What a child with gender dysphoria needs from the adults in her or his life is kindness but also to be told the truth: nobody can change sex. The various medical procedures on offer won't achieve that and will necessitate lifelong treatment which often has adverse effects on quality of life, physical and mental health, fertility, sexual response and life expectancy.
A young child can't understand much of that, but should get skilled and sensitive help to work through the key questions: you are a [boy/girl] and you will grow up to be a [man/woman]. What is it about being a [boy/girl] or growing up to be a [man/woman] that is making you so unhappy? What can we do about that?
The parents and guardians need that help as well. So many case histories of dysphoric children mention parents who can't accept a gender nonconforming child, homophobia at home or in the local community, a parent who always wanted a child of the opposite sex, parents who seek help and are told (and in their frantic worry accept) that what a distressed child says must be taken literally - in this one instance.