If the Chinese get their "carrier killer" DF-21 missile to work, by solving the targeting and tracking problems in order to get their ballistic missiles to the general area of our carrier so that radar on the missile itself can home on the target, it will force us into predictable counter-measures that China won't like:
Andrew Erickson, a professor at the U.S. Naval War College who follows China's ASBM development, said that the Second Artillery, China's strategic missile force, "already has a capability to attempt to use the DF-21 D against U.S. carrier strike groups, and therefore likely expects to achieve a growing degree of deterrence with it." Other analysts say that even if the ASBM is in the early stages of deployment, there is still enough time for the U.S. to develop effective missile defenses or take other countermeasures.
However, some of the latter would be profoundly destabilizing. The warhead of the DF-21 D would be guided to its target with the help of Chinese satellites, over-the-horizon radar and unmanned aerial vehicles. If the U.S. was unable to shoot down incoming ASBMs, it would have to attack Chinese missiles and radar on land, or the guidance satellites in space. This could trigger a wider war with China, possibly escalating into a mutually devastating exchange of nuclear weapons.
That always seemed logical to me. I was mostly thinking of the targets in China since I don't think taking down their satellites would be as much of an escalation--out of sight, out of mind--and because I'd think that would be one of the things China would try to do to us to mess with our fleet.
It's worse than that, as that article goes on to explain:
Indeed, if China hit and sank a U.S. carrier with an ASBM it would be "bigger than Pearl Harbor and 9/11 combined," according to John Pike, founder of the Washington-based think tank Global Security. "America would want payback," he added. "Would Beijing want to go there?"
With such high stakes involved, under what circumstances, if any, would China use ASBMs to attack the U.S. Navy?
I think we attach too much importance to our carriers, since they no longer hold a monopoly on our offensive power, but the fact is they are such a symbol of our country's power that losing one (or more) would be such a symbolic hit that we'd have to counter that impression with some serious payback.
Be careful what you wish for, as the Chinese curse goes.
