I have been rejected many times with no explanation.
I think sometimes, like any competition, what I wrote is just not the best of what they had to choose from at the time. They can't publish everything, some editors say they cannot publish 1% of everything they receive, so there is no 'reason' I got rejected that is specific to what I wrote: I am in the same pile as dozens of other people, rejected because some other author wrote something more compelling than me. I got rejected because I wasn't the best thing they read that day.
If you have a specific venue that you want to get into, like a newspaper or particular publishing house, one way to learn anything from that is to try and figure out what the editor IS publishing. Imagine you are trying to learn how to predict what topics they like, the style they like, whether they like simple sentences or complex ones, whether they like highly educated language and grammar or more common language and grammar; similarly the education level they like their writing at. Does the political writing they accept tend toward the middle, or one end of the spectrum? Do they like emotional words and content, or do they prefer dry and emotionless prose? If there is humor, what TYPE of humor is acceptable, and what do you NOT see? For your newspaper, do most of the published authors seem to have credentials, like academic standing, political standing, or social standing (businessmen, school leaders, charity leaders, religious leaders, etc)?
Consider structure: the lengths of sentences, and paragraphs. The lengths of dialogue sentences.
All of these things (and any other generalizations you can think up) are metrics you can use to compare or categorize 'writing'. Some of what I mention may not apply to newspapers, or non-fiction, but I hope you get the idea.
Use such metrics to compare YOUR writing to the writing that gets published. Obviously the words are different, but you need to try and separate what your editor accepts from what they reject, and all you have to work with is what they have accepted!
That isn't as hard as it sounds; it is like trying to generalize my interests in fiction based on what what books I have bought: You'll get a pretty good idea, even though you don't know which books I have considered and rejected.
This kind of analysis may reveal why you were rejected. It may not, but if you can develop any mental model at all of what the editor accepts and prints, at least it can guide you toward writing pieces with a better chance of being published.