Both parties disagree about something and one or both parties refuse to allow the other to continue to hold the position they disagree with, even though the opposing party's opinion is not something the other party has direct control over beyond continued attempts at influencing them to change said opinion... and where "influencing" can range from simple continued argument, to coercive violence, to murder.

In practice, disagreeing to disagree typically leads to some harbored feelings of hatred for either or both parties toward the other, and in extreme cases both sides feeding off each other for even more hatred.

At a societal level, in the worst of those extreme cases, this has lead to mass atrocities such as "reeducation camps" or mass culling of "undesirables" when one group has sufficient power to enforce control over the other. Which is why any system that prevents too much consolidation of power can be an effective safeguard, but unfortunately even then there's no guarantee of effectiveness.

Philosophy has always interested me. Psychology and sociology as well, but only as long as I can keep my distance from the subject(s) of study, which is why I went in to engineering instead (well, that and the money). Things are inherently more logical than people, and all too often... well... people just suck. :-)