You really are that stupid, Fasces349.
It's quite likely that a nuclear war would start out limited, but once one side starts to lose too badly they'd go for broke. Here's a hypothetical. China plans on invading Taiwan. To ensure success they launch huge conventional attacks on American and allied bases in Japan, South Korea, and the Pacific. To make sure they get carrier groups at sea in the Pacific or Indian or wherever they happen to be floating at the time, they launch nuclear strikes in those areas. Now, it's quite likely that the United States will respond with a nuclear attack (whether tactical or all-out), but if there's still a significant conventional force left they could make use of that to punish China, or it's possible they could even surrender.
So there. There's a scenario where a limited nuclear war would be possible and make the targeting of aircraft carriers a good policy. I find it quite unlikely that this WOULDN'T quickly escalate into a nuclear holocaust (see where I said we be gone before we missed the carriers), but it's possible that China's crazy plan would work here. Nuclear states come up with plans on how to use their weapons without immediately leading to the extinguishment of humanity, it's just that in practical terms things probably won't work out that way. That doesn't make the decision to target carriers foolish, though.
I mean, what do you expect? That the opposing navies just steam out to sea to meet each other? you might as well have armies wearing colorful uniforms line up in a field and march at one another.