There were no aliens. How, then, to prepare for an alien invasion?
Not having any, the military decided to build some. Asking humans to "think like aliens'' didn't work. However, enthusiastic experimentation established that drugs, psychological conditioning, and some judicious brain surgery could not only convince those that survived that they were aliens but also twist their thought processes in quite unprecedented ways.
The war games were a disaster - the aliens always won. They knew intimately how humans thought, yet no human had ever encountered minds like theirs. Stashed away to be used as strategic consultants, lest they might lose their edge, nobody tells them they are humans. An unnecessary precaution: they are fully aware of their physiology and life histories, which doesn't clash, in their minds, with their certainty of being aliens as well. Both things are true for them, both things useful in their slowly unfolding, inhumanly strange plans of conquest.