My example was obviously a gross simplification, but not all disagreement stems from contradiction. Worse, sometimes when people agree on many points they are in inreconcilable disagreement with each other on others. If we were to consider that both groups have held their position for many years, it should be immediately apparent that it would be impossible for either to change their mind. Time calcifies opinion.
You're right, though I think I would say "extremely difficult, tending toward impossible". People do not change their minds easily, especially on subjects they feel a strong emotional attachment to.
