Ask any swabbie what a couple of hits by modern missiles would do to a carrier.
This is nothing new. Look at what the Japanese accomplished with their Kamikaze tactics in WWII, which essentially made their aircraft man-guided missiles.
To show the fallacy of your argument, suppose the ChiCOMS today right now, had 11 functioning carrier BG's and we had none. How would you "feel" then?
PS: Any damage above the water line could take a carrier out of commission(for a while) it will not sink it. Torpedo damage would be more devastating but still not sink a modern carrier.