The only people who would build a nuke bomb to kill humanity would be terrorists. And most of them would probably not do that. They would also need about 100,000 nuke bombs to kill us all, and I can't see how they could hide that for long.
disease
I find that more likely. It would be devastating if AIDS started spreading as quickly as the Black Plague, but we'd need many other deadly diseases to come quickly after it to kill us all.
what about another Bg Bang? If it builds it destroys
You're probably suggesting the Big Crunch, which states the universe will stop expanding and collapse (But it will take a few trillion years). Not likely: Earth will most likely be destroyed by the end of the Sun's life into Red Giant phase, or something happening that destroys the Earth else how (Ex: Super massive black hole). The other theory is that the universe expands and collapses in a cycle, and if it were to collapse in our lifetime, we'd already be dead before it turns into the Big Bang (How would you survive in a spot as heavy as the universe, and smaller than an atom?).
nuke will never destroy the world. If any country tries to nuke another country the United States will jump in and stop it. also no country should be stupid enough to start a war like that
People under estimate paranoia. I wouldn't put nukes pass as a potential end of our world. Under the right pressure and paranoia I can see nukes exterminating mankind.
I think if a bunch of nukes went off for some reason then a pandemic happened man kind could die. But not one without the other, and the probability of that happening is kinda slim.