To me, the most unreasonable thing about most post-apocalyptic fiction is how few Humans have survived and rebounded in the wake of whatever catastrophe has befallen Earth.
Our entire history as a species can be summarized in three words: "Humans never stop."
We've experienced terrible challenges many times throughout our relatively short time on this planet, and we've managed to withstand them all. This is because Humans are a textbook example of an invasive species. We have few (remaining) natural predators, we can eat almost anything, and we can improvise ways to withstand the climate itself, as well as makeup for our own biological shortcomings. We also have the most powerful tool in any arsenal: teaching. Each new generation of Humans is collectively smarter than the previous allowing us to completely change our way of life in just a few generations, far quicker than normal biological adaptation would allow.
So let's take a look at all of the things that have threatened to destroy us over the millennia. The first big threat came from the climate. The Ice Ages (which are still in effect) had a deadly impact on our species of fur-less apes. Our ancestors weren't accustomed to the frigid cold of Europe and Asia, and we responded by mastering fire and clothing. Fire was a big step for us, especially since fire may be the reason Humans are Human. Fire allowed us to cook food, releasing much more nutritional value than raw food. Better food meant more energy to spare for brain development, which may be linked to our spectacular rise in intelligence that occurred around 1.8 million years ago. The cold didn't limit us, it forced us to improve.
In a non-climactic sense, another major threat to humanity was disease. We've faced off against Smallpox, Polio, Tuberculosis, and the 1918 Flu pandemics. Perhaps the most devastating was the Black Death. Sweeping across Eurasia between 1346 and 1353, the plague killed approximately one-quarter of all people on Earth, reducing global populations from an estimated 450 million to 350-375 million. The European population was reduced by anywhere from 30% to 60%. The world didn't fully recover from the plague's toll until the 17th century, 300 years later. But we did recover. In fact, the devastation caused by the plague in Europe may have indirectly led to the societal restructuring of the Renaissance and Enlightenment. We might very well have turned our tragic losses into gains.
One of the most commonly used causes for fictional apocalypses is disease. Whether it's zombies or death, the disease is always shown to wipe out around 90% of the world's population or more, leaving bands of struggling survivors to pick up the pieces. Simply put, a disease like that would be terrible at its job. Diseases thrive in living creatures, not dead ones, and if a virus or bacterium starts killing too quickly the culprits will die before passing on their traits to the next generation. This is why deadly outbreaks tend to be extremely short-lived. The bottom line is that a disease killing most people on Earth would require extreme luck and very little hand-washing.
The only time we've ever come close to total destruction was during the Cold War, and that was at our own hands. The only time in our history that our existence as a species was threatened was at our own hands. We collectively put the gun to our heads, and collectively we put the gun back down.
Humans are like water. We can't be compressed. Each time we face pressing harm we find ways to flow around the danger and continue living our lives.