Dual-type moves just seem kind of messy to me. I guess they could make it so that if only one of the types is super effective, it gets a 50% boost rather than a 100% boost. Similarly, if only one of the types is not very effective, it would result in a 25% reduction rather than a 50% reduction. If the two types conflict in effectiveness, it would probably just even out. When paired with dual-typings, this creates a dizzying array of possibilities.
An alternative, suggested by Count Bleck, is that moves could have multiple hits, with each hit having a different type. For example, Eruption might have a fire attack followed by a rock or ground attack. In this case, the first attack might even be physical, while the second is special. This seems plausible, but I doubt that such moves would be terribly practical.
And in regard to the arguing, I have only this to say. Pokemon is clearly a game designed for sophisticated and intelligent men and women with adult tastes. I am sure that Game Freak, whose opinions we all hold so dearly in our hearts, would expect that its target audience be capable of conducting civil discourse on the matter of their Pocket Monsters.