Part of the issue here is that TERFs (pretty much by definition, given the acronym TERF itself) don't believe that trans women are women and that trans men are men. To them, the adjectives "transgender" and "cisgender," placed before a noun like "woman" or "man," threaten that perspective. if a transgender woman says, "Hi, I'm a transgender woman," the TERF may twistily interpret her statement as invoking a third-gender category that is neither-woman-nor-man: transwoman, as it were. But if that person adds, "—and you're a cisgender woman," it alarms the TERF because it implies there could be a type of woman other than a cisgender one. The very term cisgender woman suggests that transgender women are women too. This implication is not acceptable to TERFs. That's why they don't want any adjective before "woman" or "man" modifying what type of woman or man someone is—not if it's validating transgender people's self-designated gender. TERFs do not like the adjective "cisgender," not so much because of what it says about them (it only says they're not transgender!), but because it implies that "transgender" is real. It's the other side of the coin they're worried about.