well, just because some of our premises are wrong doesn't mean the conclusion is wrong. We can be wrong on facts, causes and effects, etc.
I think when each person admits they're wrong, more people would be willing to do the same. And instead of arguing, more discussion would take place. Arguing itself isn't a bad word but has so many negative connotations in our society. And admitting we're wrong is essential to having discussions. Otherwise, they'd be like debates where each person only knocks the other down and no one really learns to improve themselves or their views.