Their serious anti-ship weapons are their submarines, one of which not too long ago sank the South Korean warship the Cheonan.
And with all the other submarines out there, our aircraft carrier fleets need to make it abundantly clear any non-US submarines that approach them, no matter from whom, are subject to being sunk with no further notice.
No warning shots.
They don’t always know about subs.
A few years back the Chinese surfaced a sub inside a carrier group, nobody saw it til then. Diesel electric is quiet.
The point is, nothing is invincible, and we should not underestimate anyone.