Russia and China both see a missile defense system as a threat to their security, since nuclear security today is still predicated on the idea of mutually assured destruction. If America is able to protect itself from nuclear devastation and other countries are not, we hold a distinctive upper hand. Such concerns aren't supported by the scope of proposed missile defense programs. The idea of creating a missile shield that would be able to undermine Russia's vast nuclear arsenal or make America invulnerable remains a pipe dream. A limited defense system would also be able to intercept and neutralize accidental launches, which is something that low-tech nations may be susceptible to.
Foreign policy is largely an exercise in psychology.
Nations are constantly trying to guess what the leaders of other nations will do and craft policies that achieve goals based on those predictions. The air war in Kosovo was a game of chicken in which the State Department and NATO guessed wrong on what Slobodan Milosevic would do when faced with a bombing campaign. Proponents of a missile defense system assume that rogue nations with access to military nuclear technology will use missiles to attack the United States. Rogue nations aren't going to bother with missiles except to make us worry about an attack from the air. It's far more reasonable to conduct an attack through terrorist means by smuggling small warheads into enemy nations.