It is not clear why, since they espouse no objective beyond protection against the same terrorist states. Yet only Russia and China have something to fear from an American anti-ballistic missile. Russia should fear because the one piece of the Cold War that remains in place is mutual U.S.-Russian deterrence based on the chance that even a surprise attack by one huge arsenal on the other would leave enough surviving missiles for terrible punitive retaliation. But, with everything else in Russia having deteriorated, the number of survivable missiles probably has, too, and the small Clinton defense might suffice to cope with these, thus ending historical Russian deterrence. Even the possibility must cause Russian nightmares.
China has many fewer missiles.
China is going to increase its missile force anyhow. Faced with an ABM, it will probably do so faster, to nobody's benefit. America's European allies oppose ABM out of nostalgia for the good old debates of the Cold War. In the course of 30 years the two sides of NATO worked up a panoply of theologies about the circumstances in which the United States would really risk its own existence in using nuclear weapons to defend Europe. The debate continues, even though Europe is no longer threatened by a major atack from anyone.