The removal of nuclear weapons is an important objective in our world for several reasons. Let me mention three of them.
First, the threat of nuclear warfare is an alarming one. Moreover, we have more than enough nuclear weapons to destroy the world several times over. So, disarmament is a step in the right direction.
Second, we need to be careful that these nuclear weapons do not get into the wrong hands. For example, with the collapse of the former Soviet Union not all nuclear weapons might be in safe and responsible hands. What happens if a rogue state gets a hand on a nuclear weapon? This could create havoc. Removal of nuclear weapons, therefore, is important.
Third, nuclear energy should be called into question. Just think about what recently happened in Japan with their nuclear reactors. Dangers abound.