Sure, we have counter-measures to have a chance of defeating enemy capacity to strike our carriers.
But really?
But the observation that the enemy has a missile or torpedo that can kill a carrier only begins a conversation about carrier vulnerability. Shooting anything at an aircraft carrier is a costly, difficult operation.
And beyond the monetary cost, launching an open attack against an American carrier strike group, with its own cruisers, destroyers, and submarines, is almost certainly a suicide mission.
So there are two questions that remain for anyone who thinks they even have a shot at taking down one of these enormous steel behemoths.
Can you do it? And even if you can, is it worth it?
I think the notion that something that floats can't be sunk is ludicrous. Some believe that. At least the above defense doesn't go that far. But it fails anyway because even if a carrier truly is unsinkable, that's not the metric to judge carriers by.
In any likely scenario, a mission kill is 99% as good as a sinking. And given the importance of the carrier and the psychological impact of taking one out, you are absofreakinglutely darned right an enemy will make the effort.
Especially if we go out of our way to place them in really stupid positions within easy reach of enemy attack assets. But no worries if the ship can't be sunk, of course.
Also, I would be remiss if I failed to note that carrier defenders and critics too often argue apples and oranges about two separate and distinct missions.
Why spend so much for half of the reason we have carriers by pretending the carrier is vital for all of the missions?
UPDATE: In related news:
China has launched its first aircraft carrier built entirely on its own, in a demonstration of the growing technical sophistication of its defense industries and determination to safeguard its maritime territorial claims and crucial trade routes.
I suspect China is building a carrier fleet just as carriers are becoming less relevant to sea control missions given the rise of networked surveillance and cheap precision weapons.
Big carriers look good in peacetime and are useful for war against non-naval/air powers. But in war they will be put out of action just like ours can be.
My main worry in war is that our Navy could be distracted by the shiny object while the Chinese sacrifice their carriers to achieve their objective.