When you get rid of Pokemon from your PC you don't "delete" them - you release them into the wild. What would GameFreak's excuse be for allowing to get rid of eggs? Saying you make an omelette out of Pokemon eggs would be a little much for a kids game, don't you think.
I think that since there is no plausible explanation for what happens to the Pokemon eggs when you get rid of them, GameFreak has just made it so you can't get rid of them at all (at least until they hatch),
Yes it is the same in X and Y, if you are wondering. This is also exactly why I hatch all the eggs I receive, even if I have already gotten the perfect Pokemon.