The subject area you're looking for is concrete vs. abstract thought.

Understanding the example, but not being able to generalize it to a larger question is a good example of concrete thinking.

You want to learn how to think more abstractly. I've read that the majority of people are more comfortable with concrete thinking, but that we can learn to think more abstractly with practice and tutorials.

If you google "abstract thinking" you'll find much useful info on this subject.

Personally, I find the subject fascinating. After a head injury, I had to relearn how to think abstractly. In time, it came back to me, but in the beginning I was stuck. The neurologist told me that head injuries, even small amounts of alcohol, some medications, street drugs, marijuana, bad nutrition, aging and boredom combined with lack of curiosity can all push a person toward concrete thinking.