Dennis Prager asks this question Why the “T” in LGBT? Paraphrasing his answer: the Transgender people stand for the proposition that male and female are interchangeable, that all distinctions based on gender or sex are arbitrary. Prager sees this as being of a piece with the Left’s desire to obliterate all kinds of distinctions.
I would add this: I think the Transgender people stand for the proposition that a person can choose every aspect of their identity, as opposed to the idea that some things are given to us by nature. I think this fits in with the distinctively modern idea that there is no intrinsic good, apart from human willing.
Read Prager’s whole article here.