Why?
Because what those pronouns imply about the reality of their sex is a false implication.
If I were to make a linguistic compromise, I really would accept everyone who wants to be referred to with they/them pronouns if we could just stop it with the people who want to be referred to with he/they or her/ they pronouns.
Seriously, how am I even supposed to construct a statement about you?
"Jane got out of their bed at 7am. Jane then combed get hair and brushed her teeth and got ready for work. They grabbed their (maybe her) car keys and they were on her way."
I mean, seriously, this makes no fucking sense.
I would argue that, even if those who list her/them pronouns would claim that it's just to say that they're cool with either set, it's a lie. You don't make that effort if you're cool with however people refer to you. It's still an effort to dictate language and how people refer to you. All it is is an abstraction and complication of language for your own sake.
Still, I don't entirely dismiss the singular "they". I'm not gonna wag my finger at somebody who says, "Everybody needs to turn in their homework." I'm also aware that if you refer to the Bartender, the Unmarried Mother, and Jane in reference to All You Zombies as "they", it could be argued that you're using a singular they.
The difference is the pronouncement of the pronouns by that singular individual.
It's a social construct that tells us that shouting the N-word in Harlem isn't a good idea. It's also a social construct that snipping off girls' clitorises is a good thing.
That doesn't mean that we can't say that those social constructs are objectively right or wrong.