As a former reservist 0331 Marine and a former Air Force intelligence officer, I can relate. I run into people all the time (mostly men but sometimes women) who object to the term cisgender.
Usually, I find these people have at the foundation of their disapproval the idea that transgender people don’t really exist, that gender isn’t a thing apart from biological sex.
So, by objecting to the use of “cis” they’re actually objecting to “trans.”
Sometimes people are sensitive to change, though, and haven’t actually formed any firm opposition to gender variance. They just don’t like new vocabularies.
I don’t know where your friend fits, but you’re absolutely right that “cis” is a value-neutral prefix. Perhaps explaining that to him clearly can help.