We know that most people don't hold that view because that's what polling reveals, even in the countries where law and policy have been changed in favour of that view.
To further explain my linguistic point though, it's really down to an ambiguity as to whether "trans woman" and "trans man" are meant as compound nouns (in the open form, as the closed form, e.g. "transwoman", doesn't have this ambiguity) or noun phrases.
As compound nouns, these have the sense of a man or woman who wishes to be the opposite. That is, a "trans woman" is a man who desires to be a woman, and a "trans man" is a woman who wants to be a man. They may even end up believing themselves to be so, based on that desire.
As noun phrases, these apply the adjective "trans" as if a subset of the group the noun is describing. So a "trans woman" is understood as a woman who is male, and a "trans man" as man who is female. But this only works if you also believe that "woman" and "man" are "gender identity" categories that one can identify into, rather than based on the material biological reality of being, respectively, female or male.
Introducing "cis" removes that ambiguity, implying noun phrases rather than compound nouns, and thus implies acceptance of the "gender identity" belief. When people object to the terms "cis woman" and "cis man", they are expressing a rejection of this belief system.
It's different though, in that this adjective redefines the noun it's being applied to, away from the usual understanding.
Consider "homosexual woman" and "heterosexual woman". Both describe an aspect of "woman" - her sexual orientation - without changing what "woman" means.
Compare "cis woman" and "trans woman" though. The former refers to a female and the latter to a male. This changes "woman" away from the sex-based definition that the vast majority of people understand, to one where a subset of men claim to be women.
So by using "cis", this implies an agreement with this world view that men who call themselves women somehow actually are women. A view that most people don't actually hold.
This is also why in radical feminist circles they prefer terms like "trans-identified male" instead of "trans woman", to avoid adopting the linguistic contortions of the oppressor.