I think your method is great for black and white situations. If arguing over 2 + 2 = 4, then yes get to the point. How many arguments really go that way though? More often than not arguments boil down to each persons experience and opinions formed through that experience.

It is also important to remember that emotions are always involved. If there was not any emotion why would the discussion be happening in the first place? Presumably both parties care about what they are arguing for.