Thank you
The reason trans people use “trans man” and “trans woman” – and don’t use “transman” or “transwoman” – is to make clear that “trans” is just an adjective describing one aspect of their being men or women, and doesn’t define them entirely. The same way one wouldn’t say that someone is a “gayman,” a “blackman,” or a “Chinaman.”
And as I’ve seen trans people explain it, I just think of “cis” as a shorthand way of saying “not trans.” It’s not an identity, necessarily, just a descriptor, to put the two (trans and non-trans) on an equal basis, and not have a rhetorical paradigm in which “normal,” non-trans, people are just “people,” whereas trans people are the only ones set apart with an adjective. Like “straight” as opposed to “gay.” Until gay people started using “straight” to mean “not gay,” it didn’t have that meaning in common usage. As I recall, it once was used as “straight people” vs. drug users. Or “straight” people vs. the counterculture.
Apologies, Consolation. I misunderstood your meaning and thought you meant that you would identify someone based on the gender they appeared to be.
Of course it’s not a requirement to label yourself as cis, or to claim that in conversations with others. But nonetheless, it is the term for people who identify with their biological sex.
Be that as it may, there are many examples here of people not wishing to adopt a recently-invented term to describe themselves even though it is found convenient by others.
On a related question, which I find interesting, how do people feel about being called “Anglo”? Several years ago I was participating in an online survey site, based in California. At some point, there was a series of questions about ethnicity, and possibly race. I don’t recall all of the details now, but I do recall that the term offered that was obviously meant to apply to me was “Anglo.” I had never encountered this before, and I recall feeling not only taken aback, but irritated. My ancestry is Scandinavian and Celt, not English, and as a matter of fact the Celtic part of me has historically been very much at odds with the “Anglos.” 
Huh, that’s interesting - and really unusual, since I’ve never heard that term to describe ethnicity (other than WASPs). I wonder what non-English ancestry Europeans/white people would select? Is there a “continental European” ethnicity? I thought ‘white’ was just everything, but I guess not!
And don’t get me started on the Celtic issue. It’s so hard to pin down what or who the ancient Celtics are/were - especially when I’m pretty sure I have Celtic ancestry, but in one of the more ‘controversial’ or debated regions. Who knows? 
ETA: Apparently, the term [‘White ethnic’](White ethnic - Wikipedia) can be used to describe those from “Southern, Central and Eastern Europe, and the Caucasus”? That seems really weird and contradictory.
I think “Anglo” in that context is short for Anglophone. Although of course many Latinos in California have English as their mother tongue.
Ha! I have a good friend who lives in Amish country and everyone who isn’t Amish or Mennonite (including her) is called “English”.
Consolation, I guess I’m not quite understanding your position here. Let’s say you and I are having a conversation about women. Some women, like me, were born into our gender. Some women, like Laverne Cox, were born into the other gender but are now women. We want a term for the first group. If the adjective is not “cis,” what is it? The concept exists, so we need a word for it.