I now understand the diabolical dilemma! Before this, I have made mention to Schrodinger's cat, and pointed out that a being cannot be both living and dead at the same time. I realize, of course, that the analogy is about the quantum level, and the so-called contradictions and uncertainties that happen there. Still, I had heard people say that a real cat hypothetically could be both alive and dead at the same time, which is obviously not true.
Today, however, the full force of the dilemma hit me. The problem is not that a cat can be living and dead at the same time; the problem is that for a certain period of time, you will not know whether the cat is alive or dead. Now what would be wrong with not knowing?
Many things, to be sure, but one downsides strikes me with particular force: If you don't know whether the cat is living or dead, you can't operate on either assumption. You have to prepared for either possibility, which often is more terrible than facing either option separately.
If the cat is killed before leaving the box: Then you are not likely to start caring about it, just like you don't really care that much about roadkill. If the cat is dead, maybe you'll bring a shovel to bury the poor dead thing.
If the cat is not killed before leaving the box: Then you are more likely to feel relief that the cat wasn't harmed. You might actually care about the kitty, with it's soft paws, big expressive eyes, and even desire to adopt it, so that it won't have to be subjected to any more of these terrible experiments!
Neither of those are particular terrible options. But look what happens when you put those two together:
If the cat may be dead and may be alive: Then you start to care about the kitty, imagining it to be alive, and fear for it's safety. You start to wish that you could adopt it and protect it from these sorts of dangerous situations, but fear that it's too late, and that the kitty has already breathed its last. You have a shovel in one hand, and a collar in the other. You can't be content with the cat being dead, because you don't know that it's dead. You can't be relieved that it's alive, because it may not be!
It it this indefinite state of mental torment that is the real and insidious dilemma represented by the idea of Schrodinger's cat.