This reeks of all-or-nothing thinking, which itself reeks of deep insecurity (a very likely root condition of being disagreeable).
It's one thing to have differing thoughts and opinions. It's another thing to be "disagreeable", which is the personality trait of being difficult to work with, often for the sake of being contrarian or having an ego trip (i.e, proving that you are right to showcase your power and value relative to others).
As others have stated, disagreeing is orthogonal to being disagreeable. One can disagree via constructive dialogue and open communication; however, taking disagreeableness as an identifying personality trait (and moreover, holding it as valuable in-and-of-itself) is a slippery slope to the creation of toxic working relationships.