Okay...

Say you want to test principle X (a principle of ethics or rationality or whatever you like) and see if it gets a good answer in every case. You have some choices: you can try to test every case; you can use the principle for a couple of weeks and see if it encourages you to leap off of anything tall or open fire on a daycare; you can come up with a couple dozen likely situations that might call for a principle like the one you have in mind and see if it does all right; or you can do your absolute best to destroy that principle and find a situation somewhere, somehow, where it flounders and dies and tells you that what you really should do is wear a colander on your head and twirl down the street singing Gilbert and Sullivan transposed into the Mixolydian.

Weird situations like those in which Omega is invoked are attempts at the last, which is usually the strategy quickest to turn up a problem with a given principle (even if the counterexample is actually trivial). The "attempt to destroy" method is effective because it causes you to concentrate on the weak points of the principle itself, instead of being distracted by other confounding factors and conveniences.