Reality is that which remains the true when you cease to believe in it. If a transgender person ceases to believe that they are a member of the opposite sex (as it does in a majority of cases), do they remain a member of the opposite sex? Under any standard no. Therefore, according to the definition of reality, they are not really a member of the opposite sex, it is just a delusion.
Thus, I have proven from first principles that transgenderism is a delusion. There is no higher form of evidence than a proof form first principles. The only way to falsify my proof is to provide an alternate definition of reality.
Trans people don't think they're the opposite sex, they identify with a gender other than the one socially related to their birth sex, and often but not always feel psychological distress at their physical body deviating from the socially prescribed normal for that gender, so your explanation fails at the level of base understanding of the topic at hand.
Sounded fancy tho, so that's nice