Outside Issues

In principle, disagreements are generally because of: misunderstandings, differing values, or outside issues. Misunderstandings and differing values can generally be resolved within the group. When a disagreement is caused by an outside issue that has nothing to do with the issue at hand, then it must either be dealt with outside the group or someone might end up losing, and that might be okay.
An “outside issue” is a disagreement because of, for example, some incident between the parties that happened years ago and has never been dealt with, or because of a mental disorder such as an addiction which is warping someone's judgment or behavior. Or perhaps it is because of a misconception closely held since childhood, or an unreasonable fear. Outside issues are usually personal and are often completely unrelated to the group's immediate business.
If an outside issue is in the way, agreement will only come if the issue is dealt with. If it is not dealt with and the disagreeing parties cannot let go, than the group might get paralyzed by an issue they have no ability to fix.
Practical Tip: Once you recognize that an outside issue is the cause of a disagreement, encourage the parties to deal with it outside the group. Perhaps therapy is called for, or mediation. If they are unwilling or unable, take a vote or hire an arbitrator or
somehow otherwise resolve the issue even over objection. Losing is not always bad. Sometimes it is the only thing that will allow some people move forward. It is better that one or two people lose a single issue than the group as a whole gets stuck and unable to make progress.