Nuclear warfare is very unlikely since 95% of nuclear bombs are in the hands of the US and Russia, neither of which are even close to considering using them anytime soon. In fact, the chances of it happening were in the Cold War -- the Cold War passed and nothing happened.

If you look at the data, you can actually see that war has been on decline for ages now and all of humanity's major killers -- famine, war, homicide, plague, disease, genocide, natural disasters, child birth, etc -- are trending downwards. Humans are surviving more frequently and living longer lives than ever before; if we haven't been extinct yet, the chances of us going extinct now are even lower. In fact, since the start of civilization ~10,000 years ago, not a single event has even come close to killing of 2/3 of humans, let alone 100%. Wars between major powers have not happened since WWII (proxy wars sure, but never direct war between the two) and according to almost every geopolitical analyst, the chances of this happening in today's interconnected world are near non-existent and the chances are decreasing by the year.

Not only that, but even if we take the most far fetched idea and assume there was a nuclear war, it would never escalate beyond a few warheads, not even 1% of the world will be killed off. Millions will die and and hundreds of millions more will have their lives changed forever, and every person on Earth will be affected one way ore another, no matter how minor -- but even then, it's not even close to killing of homo sapiens. Hell, while we're at it, let's just say that every nuclear bomb in the world is detonated at the same time spread evenly across the globe. Will homo sapiens diw then? Nope. The immediate blast radius will affect but a tiny fraction of the Earth's surface, the real damage comes from radiation, debris kicked up into the atmosphere. Society will collapse, most humans will die (mostly from the chaos), radiation is far from killing humanity but it will make many people sick and mess up food chains, and the debris will cause a minor "nuclear winter" but humanity will survive simple because even though most have died, it's not extinction until everyone has died. The few that remain will reproduce and society will start back up again within centuries. Same thing goes with an epidemic and asteroid impact. Humans are like bacteria in a way. Most anti-bacterial sprays kill "99.9% of bacteria" because killing off 100% is impossible. The few that bacteria that survive are enough to prevent an extinction and reproduce and build the population back up again.