@Phaedrus, I don't think you have to go as far as war to see the either-or fallacy in action. People do it every day in one form or another. When there are two possible outcomes to a decision, one is usually positive and the other one negative. Either we'll make the right decision and earn a reward, or we'll make the wrong decision and suffer the consequences. When people are only presented with two choices, they are almost certain to choose the one with the greatest benefit or the least amount of damage.
In the book "Zen and the Art of Motorcycle Maintenance", the narrator discusses being on the horns of a dilemma. If a person encounters an angry bull, he may believe he only has two options: move to the left or move to the right. Either way, he's going to be gored by the bull. However, the person still has two other options available. One is to throw sand in the bull's eyes, rendering him helpless. The other option is not to get into the arena in the first place.