Kim Jong-un has two audiences for his utterances. One is the international community. The other is the domestic community. The problem there is that the domestic community wants him to project strength and confidence. If he claims that the North Korean military is powerful and the match of any military in the world, it doesn't sound true if someone outside North Korea (e.g. Donald Trump) then says something like
However, I would like to know in what situation would it be likely for North Korea to actually use nuclear weapons? I can't see any situation that would not lead to their complete destruction.
A situation could easily arise where Kim believes that he has to use nuclear weapons to demonstrate to domestic parties that he can.
It's unclear what he expects will happen in that situation. Will the United States nuke North Korea? China wouldn't like that. Perhaps Kim might think that that would be enough protection.
Nuclear weapons aren't instantaneous. North Korea could do considerable damage to South Korea and even Japan in the minutes between launch and explosion. Some of the damage might occur after North Korea was destroyed, but that's cold comfort for those who might die as a result. As more and more time goes by, North Korea can build more nuclear missiles. So this becomes more and more dangerous.
If China convinces the United States not to use nuclear weapons, a conventional invasion allows the North to do even more damage. Plus, North Korea actually has more people with military training than the United States does. Most external parties believe that the United States has better (more expensive) equipment that will overcome that. But it's possible that Kim doesn't see it that way.
There is nothing that keeps Kim from being wrong. And we have no idea what he thinks. He recently responded to a Donald Trump tweet by saying that North Korea could destroy the United States. What if he really believes that?
Given this, why is there so much concern for North Korea's nuclear program?
Apparently you, I, and probably 99% of the people who are reading this may regard that viewpoint (that North Korea could win a war with the United States) as nuts. But can we say that Kim does? If so, he isn't saying it publicly.
Even if not, what happens if Kim dies? His successor might be someone who actually believes his rhetoric.
Have you ever been in the middle of an argument and said or did something that you knew was wrong? Just because you were angry? Later, you regret it, but it's not like you can take it back.
Now assume that you have nuclear weapons and have created a system where everyone has to do what you say or risk terrible consequences. You don't have a system of two people turning keys to authorize a launch. You can do it alone.
Sure, using nuclear weapons might be stupid. But how do we know that Kim won't be stupid? It only takes once.
What happens if North Korea builds as many nuclear weapons as China has? What if they build as many as either the US or Russia? Then they too could do things like invade South Korea. Or Japan. Sanctions? Those haven't stopped them so far.
Perhaps you believe that North Korea would lose a conventional invasion of South Korea. Perhaps you are right. But do they believe that?
I don't know that either South Korea or Japan would solve North Korea's problems. Yes, they are richer. But that would tend to change if they were suddenly part of North Korea. They trade for the same things as North Korea needs. But again, is that how North Korea sees things? South Korea is part of historical Korea. And Japan was their last conqueror. Both are richer than North Korea, which they might naturally resent and blame on outside forces.
Again, even if they are wrong, that doesn't matter to their perceptions. And it's their perceptions that determine their actions.
If there were a rebellion, Kim might use nuclear weapons domestically and then claim that the destruction was the result of foreign action. Once that story was issued, there would be great pressure for him to "respond" in kind.
Eventually he might feel that the risk of international defeat is less than risk of domestic insurrection.
Japan lost World War II. They're doing pretty well now. Perhaps Kim doesn't regard losing as being as dangerous as others see it. Doubtless he has a nuclear bunker. He might lose millions of citizens, but it's not like he can afford to feed them anyway.
Let's assume that Kim believes that actually using nuclear weapons would result in his destruction. Are there any ways that he can gain from nuclear weapons without using them? If he had had nuclear weapons two years ago, ISIS was much richer then. They could have traded oil to him in exchange for one or more nuclear weapons. Then they just need to smuggle it to the right location and boom.
This leaves the west really mad at ISIS. No skin off Kim's nose so long as they don't realize that he had anything to do with it.
It leaves Kim with his own oil that he didn't have to pay real money to get. He just had to build a device.
So what if a million westerners died? From his perspective, that might even be a good thing.
Maybe if they are distracted by ISIS, the western powers would rather buy off Kim than engage in sanctions.
North Korea might use a nuclear weapon in such a way as to make it look like someone else used it.
Maybe they don't get away with it. But if they think that they will, they might do it anyway. By the time they find out they're wrong, they already did it.
There are multiple ways that North Korea could end up using nuclear weapons. Saying that such use would be a bad idea affects but does not eliminate that. It's also unclear if North Korea agrees as to the consequences. And perhaps they think that they can use nukes without anyone knowing that it was them, either covertly or through sale to a third party.
Why were people concerned about nuclear war during the Cold War? Both sides had enough weapons to destroy the world as we know it. Obviously that would be a bad idea. But the US and Soviets still engaged in decades of provocations of each other.