The Cold War
One of the early causes of New Zealand going nuclear free was the fear of the potential third World War. New Zealander's were afraid of the nuclear threat due to the arms race between the Soviet Union and the United States. The nuclear arms race was the rivalry between the two superpowers for nuclear warfare control during the Cold War. The whole world had seen the destruction the United States caused to Hiroshima and Nagasaki when they dropped the atomic bomb, which ultimately ended World War II. Many New Zealander's were not happy that two of the most powerful nations were in possession of such detrimental weaponry. During the Cold War period a state of Mutually Assured Destruction (MAD) was in place, this meant that if one side were to attack the other the consequences would be catastrophic to themselves, which hypothetically would prevent both sides from attacking. This meant that if the Cold War turned in to the third World War, it had the capability to be a nuclear war, and if the Soviet Union or the United States used it's nuclear weaponry it would cause global demolition.
Above - Nuclear warheads post WW2: This graph shows the nuclear warheads secured by the United States & the Soviet Union from 1950. From this graph we can see that both sides were unaware of the capacity of the enemy's nuclear weaponry, which is why, during the nuclear arms race a state of MAD was in place.
As a result of the fear of a nuclear World War III, protests against nuclear weaponry began in New Zealand in the 1950's. In 1959 the Campaign for Nuclear Disarmament (CND) was formed in New Zealand. One of the groups most successful protests was the 'No Bombs South of the Line' petition in 1963 which gained over 80,000 signatures from New Zealander's. The government did not act on the petition as ANZUS was an important ally to the National-run administration at the time. After the petition was turned down by Parliament, a lot of the public interest was lost and members of the New Zealand CND had started protesting the Vietnam War.