A good deal of long-standing arguments are due to both sides having conflicting HiddenAssumption(s). An assumption is hidden if you take it for granted, often believing it is CommonKnowledge?.
Knowing that an argument is based on conflicting hidden assumptions doesn't mean the argument will suddenly go away (or the parties will stop arguing). Many hidden assumptions are emotional in nature. Others are embarrassing to admit that they were wrong all along. Some are unverifiable, and so it's just a matter of opinion (we could all be brains in vats; most of us assume we aren't, but there's really no way to confirm this).
See also: CulturalAssumptions, AmericanCulturalAssumption, UnitedStatesCulturalAssumption, AmericanComputingAssumption