First, this is not my definition, but the WPATH's, which I'm sure they've come up with after a great deal of study and deliberation, using teams of experts in the field.
And second, don't you think that when a birth male wants to see himself looking like a woman in the mirror, it is because there is a part of his identity that differs from the sex assigned at birth? Why else would he gain so much pleasure or satisfaction from seeing himself looking feminine? Males who have solid male core identities do not want to look or feel feminine.