Fighting oppression according to a cis/trans axis of gender, rather than by male/female social-role-assignment, requires subscription to the belief that humans have something like an internally calibrated “gender identity compass.” This “gender identity compass” apparently directs us toward one of two mutually exclusive (yet culturally bound) sex-based social roles.
“Cis privilege” theory is predicated on the assumption that if the orientation of each individual’s “gender compass” matches their sex-based gender role assignment at birth, they are privileged by gender. If it doesn’t, they are oppressed by gender. Using the word “cis” to describe non-trans people’s experiences of gender is a concession to this essentialist position about the internal source of humans’ “gender identity.”
By definition, then, to be “cisgender” is an unproblematic state of experiencing gender because it means your sex-based social role assignment at birth is in harmony with your True Self. To describe someone as a “ciswoman” is to believe that girl-socialized-females should (and do) experience their sex-based socialization as a series of neutral or maybe even pleasant interactions with the world. Yet the lived experiences of women and the statistics tell a staggeringly different story.
Male sexual violence against women; the persistent pay gap between males and females; and lack of female representation in democratically elected governments the world over serve as undeniable evidence that the sex-role socialization of females operates as a handicap to females’ full humanity, not as a benefit or a privilege. Many women find the notion of “cis privilege” offensive for exactly this reason. It neutralizes unequal power dynamics between males and females and then proceeds to analyze gender-based oppression according to each individual’s self-reported comfort with the social role s/he was assigned at birth. Structural oppression doesn’t work that way; it isn’t subjective and you can’t “free yourself” by changing your internal identity.