Every sovereign country in the world have absolute right to develop its military. For nukes, those who signed the UN convention willingly won't make them. Those who was denied that right by the UN, such as North Korea, may still do so but at a cost. NK can develop all the missiles it like, as all other states can. 

NK and U.S. are enemies, officially, technically. NK and SK are not enemy, but not at peace. In the 1950's the U.S. intervened in Korea civil war on the South side and killed 3 million in the North. For this NK will be enemy of the U.S. for centuries. (Ditto for Vietnam, Cambodia.) The U.S. have been looking for opportunities to restart the Korean War, to win this time. And the only way it can win is to use nuke on NK. This is why NK is developing nukes - national survival from certain American attack. They know what happened to Saddam. They know China developed nuke in 1960's to fend off certain American attack and it worked. Any enemy of the U.S. without nuke is done.