I've always postulated that there is some alien race which is holding the proverbial gun to the heads of our leaders and saying, no doubt in some curious alien dialect, "If you let the massed know the Earth is flat, we'll vaporize you all!"
Thus the motive of the government for hiding this secret is as base and instinctive a motive as possible; the desire for self-preservation and the preservation of mankind.
Now the motives for the alien's, on the other hand, I have no idea. But they're aliens, who knows what they're thinking?
Maybe some other aliens are threatening them, and some more aliens are threatening those aliens, and...