You do, actually, have to be disagreeable to disagree. Agreeable people don't like to cause a fuss and just go along with stuff even if they disagree internally. Disagreeable people are the people who tend to disagree. That's all it means. Some of them are snarky assholes (you right now?), and others are just people who disagree.
"Disagreeable" in common parlance means difficult, overly-critical, and aggressive, but that's not what 's being said here.
It's not about "passive" vs "assertive" like you claim. Both of those can be agreeable!
[1] https://arc.psych.wisc.edu/self-report/big-five-inventory-bf...
I think that being the unpleasant version of “not a yes-man” just means that people will try to find ways around you.
Obviously disagreeable can agree or disagree, and they can do either well or badly (I happen to be very good at both, thanks). It doesn't change who they are while doing it. Just like someone who isn't open to new experiences doesn't experience a personality change while trying a new restaurant.
Disagreeable people do, as a group, have more unpleasant, cynical and snarky people. But that doesn't mean that all people in that group are that way. It's not fair for you to assign me these qualities and then argue against them when I'm talking about disagreeable people at large. Again, it's half the population so there's a wide spectrum of outcomes.
-1 for strawman
disagreeing with someone and raking high on Disagreeableness BigFive trait are two different things