Carter is a graduate of the Naval Academy and a former submariner. He worked with Admiral Rickover in the development of nuclear submarines. Before the current Star Wars fantasy of a missile defense shield, the doctrines of deterrence and mutually assured destruction was used to prevent the use of these terrible weapon. In other words, no one dared use them for fear of a second strike in retaliation for a preemptive nuclear attack. If either side used them preemptively, mutually assured destruction was guaranteed with the opposing county's ability to launch a second strike. Nuclear submarines gave both sides the ability for a second strike.
While it may seem crude, it did work and there was no World War III. I have more faith in these doctrines than in a missile defense shield. No air or missile defense system has ever worked perfectly. Carter knows the destructive power of the weapons, and it is only natural that he would work to prevent their use.