Wishing one's gender different is one thing, believing it to be different is something else entirely. Such belief is delusion. If a person has both X and Y chromosomes but believes they are female, what is "broken" is their perception of reality, not their DNA.
We humans live with many unfulfilled wishes. I wish I were young, slender, and wealthy, I'm none of those things. Too bad, eh? Certainly not a reason to undertake medical treatment, or radically change my life.
Wouldn't I look silly pretending my wishes had come true? Answer: yes, I would. I know this because I see fellow oldsters trying to "pass," to be mistaken for young. I pity them.