Is nuclear war exagerrated?

Some people say that the world could end with the detonation of one nuke, which is an impossibility. Even though there are many nukes on the planet, Russia and the US have the most by far and most of the Russian and American nukes are tactical, which are capable of destroying large targets on a battlefield without widespread radiation and devastation. Humanity has more of a chance of getting wiped out by an asteroid than a nuclear war. Nuclear war has always been a threat, but it is so exagerrated that there are people that are always fearing that a nuclear war is going to happen soon and driving them miserable.