One of the most important goals, politically, to North Korea is reunification. South Korea joining the UN would have presented an additional hurdle to the two countries ultimately rejoining. This plays into the overall Cold War with the USSR and China blocking South Korea from joining.

It is no coincidence that South Korea successfully petitioned to join the UN during the political crisis of the Soviet Union. China and the US had also begun rapprochement during the 1980s.

North Korea sought UN membership specifically because South Korea petitioned for joining the UN with Gorbachev's support. North Korea needed access to the world economy due to loss of USSR support and the West believed that allowing North Korea to join the UN would help move North Korea reform along more quickly.

Source: Korea and the United Nations - Chi Young Pak Source: North Korea Reluctantly Seeks UN Seat