The "pretending to be wise" answer is that it's easier to deal with mass extinction than with individual mortality; that the thought of your own death is weakened by the thought of gigadeaths.

More seriously, though:

Major disasters have always been a large part of human cultural experience. Cities have been destroyed by earthquakes, volcanoes, or hurricanes. Within recorded history, plagues and famines have reduced prosperous civilizations to desperate stragglers living in ruins.

Preventing or surviving disasters is, therefore, one of the most important things humans can work on. Disasters loom large in our cultural consciousness because they really are large and because we can actually do stuff to make these problems less bad.

Disaster preparedness is, in fact, no-kidding, really important for you, your family, your city, your country, and the world as a whole.

Preventing avoidable disasters, including manmade ones such as nuclear war, is a major part of what makes world politics morally significant. Avoiding the devastation of war is a really good reason to get good at politics, diplomacy, peacemaking, mutually beneficial relations among peoples; and the high stakes of "shit, we could actually kill off humanity if we fuck up politics too badly" is a pretty good motivator.

So ... we think a lot about bad shit that could happen, because bad shit really can happen, and we can do something about quite a lot of it.