Upvote based only on posing an interesting question. I'd like to see more of that.
Now to answer your actual question, three examples:
Reading anarcho-capitalistic literature I learned to look at governments in a different way, talking about a monopoly on violence owned either privately as in a monarchy or publically in a democracy and the consequences the authors draws from that. How to arrive at that viewpoint? Read about the opposing viewpoint, especially in politics and political philosophy.
Reading Getting Things Done I suddenly realised why I like to do certain parts of my workflow the way I did, like putting all my thoughts into Evernote instead of scattering them on pieces of paper all over the place. The author says that the wholy system of organisation only makes sense if you trust it and I trusted Evernote to keep my thoughts where I put them. Also, implementing suggestions from the book helped to free up some mental space and I can think more clearly about other stuff. How to arrive at that insight? Read about other people's experiences solving the same problem or how they solved problems you did not know you have or you did not know could be optimised.
Reading the preface to Jaynes' Probability Theory I realised that all the scattered thoughts about how thinking could go wrong are all facets of the same problem: Deviating from a general framework of probability theory and inventing ad-hoc methods with narrow proper fields of application but misusing them. How to arrive at that insight? Read about thinking in general.
There is a common thread to all these things: Read a lot. Follow the virtue of scholarship. Learn as much as possible in a field before you try to speak about it.
A last sentence: Reading is not the only way to arrive at insight, attentively watching the world around you, thinking about your past experiences, talking and listening to people, more the old than the young, are very viable ways too, and complement each other.
Learn as much as possible in a field before you try to speak about it.
Counterpoint: You can't learn a language — including the language of a technical field — unless you're willing to try speaking in that language before you know it very well, then accept correction from those who know it better. Language learning works by trial and error, not by memorization alone.
"Lurk moar" is not actually a recipe for maximizing learning.
Sometimes our minds suddenly "click" and we see a topic in a new light. Or sometimes we think we understand an idea, think it's stupid and ignore attempts to explain it ("yeah, I already know that"), until we suddenly realize that our understanding was wrong.
This kind of insight is supposedly hard to transmit, but it might be worth a try!
So, what kind of important and valuable insights do you wish you had earlier? Could you try to explain briefly what led to the insight, in a way that might help others get it?