As long as countries keep working on nuclear technology and nuclear warfare remains such a large international issue, it seems that it's just a matter of time before one or more countries put into effect those matters to which they've devoted resources and time, and nuclear warfare takes place, though it doesn't seem to be on the immediate horizon.
I think that our demise will indeed come about through the improper or awful use of nuclear weapons. It is only a matter of time until a country or group gets their hands on or develops a nuclear weapon and unleashes it on the rest of the world and kills us all.
If nuclear weapons exist, it is only a matter of time before nuclear warfare happens. It is such a dreaded, anxiety-ridden issue and also new compared to other warfare methods, so it doesn't seem that it would happen soon, but if the technology exists, which it does, it is just a matter of time before it happens.
Mutually assured destruction (MAD). As long as the world's major powers have stocks of nuclear weapons and the capability to launch them, nuclear war is not inevitable. The destruction would be so widespread that it would be no ones best interests and would destroy the economic world we all live in.
No sane leader would commit their country to war, knowing that very same day their country would be leveled to the ground. No insane leader would be given the chance. At the moment, North Korea provides the best example of the latter: by showing a force of arms, they have lost China as an ally. If they push too far, they risk being attacked by the conventional forces of all those around them, and if they did let loose with a nuclear weapon it would most likely be shot down and the country assault by overwhelming conventional weapons.
I don't think that nuclear warfare can be considered inevitable. Is it something that we should always be worried about? I say yes. But I think we as a nation and as Earth citizens have learned about the dangers of nuclear warfare, and as such will do everything to avoid it.