Explain Like I'm Five

Aside from those in the nuclear club not wanting to share power, nuclear proliferation causes a lot of problems. It creates more flashpoints for escalating into a world-ending nuclear exchange or for non-state actors to obtain devices for terrorism, etc. The world stood at the brink for a while and decided decades ago the ultimate goal is to reduce the number of nuclear arms.

On the flip side, this is why the recent-ish invasions of Afghanistan, Iraq, and Venezuela, the intervention in Libya, and China's saber-rattling against Taiwan--among others--are serious matters. It teaches regimes around the world you will only be safe if you have a nuclear deterrent. North Korea applied that lesson, and they won't be the last at this rate.