What can destroy an Aircraft Carrier?
Without getting killed.
What you should be asking is what can destroy a carrier fleet ?
where there is an aircraft carrier , there is also a fleet including submarine escorts , surrounding it.
Most if not all enemy ships , will be detected by long range radar and intercepted by the carrier air-wings .
You get close enough to launch an attack , the carrier escorts will fire back , and you still have to deal with the air wing. The carrier fleets will also employ their defensive systems.
At this point really , it comes down to you beating the fleets defences.
You either have to slip past them or punch through them only then can you take a shot at the carrier.
the only way to counter a carrier with decent odd's is pure brute force.
while people may have delusions of sending a submarines to do that job , the odds of them succeeding may be very possible but are still fairly slim. Certainly not enough to gamble your whole national security over.
at the end of the day , you want to beat a carrier , you need to punch through the defences of the fleet. While simultaneously fending of an air-attack , or a similar missile barrage.