This may be a question as much about the study of history itself more than general history, so I'm open to a variety of ways to answer this query.
This is the article in question.
The "why" seems to boil down to "a lot of bad stuff happened." It seems odd especially because the answer is so precise and framed to be so certain. EDIT The article also seems to be rather Western-focused, doesn't it?
I think this is a function of clickbait online journalism, a hook to get you reading about climate science, tree rings and ice cores.
Also, reading the first paragraph, the precise claim seems confused.
Ask medieval historian Michael McCormick what year was the worst to be alive, and he's got an answer: "536." ..... In Europe, "It was the beginning of one of the worst periods to be alive, if not the worst year," says McCormick, a historian and archaeologist who chairs the Harvard University Initiative for the Science of the Human Past.
So, because of the way the sentence is structured, it is tough to read precisely what McCormic said. It seems plausible that he was limiting himself to saying "in Europe, worst year was 536" edit: "in Europe, worst few years started in 536", (so his claim is not what is even said in title). Which is a far-cry from saying the worst year everywhere was that particular year. And of course, that is his subjective opinion which other medievalists could disagree with.
EDIT The article also seems to be rather Western-focused, doesn't it?
I agree. The article does briefly mention crop failures in China, which hints at widespread climate effects going on. However, nothing is mentioned about what climate effects there were in Sub-Saharan Africa, South Asia, Australia, or the Americas. It is possible that tree-ring and ice core data for some or all of those regions are not yet available.
For some regions like South Asia, Ethiopia and Mesoamerica, there were writing systems which would allow accounts from the period circa 536 to survive, giving us some insight on climate, instability, warfare etc.
For other regions, including large swathes of the Americas and Africa, we are without writing for that period.
In any case, I agree with boringhistoryfan. It is a pointless intellectual exercise to determine what the "worst year in the world" was, because it is something that is so subjective. And speaking on a global scale is particularly silly if you are talking about an era prior to the current globally interconnected world.