We can teach this stuff. No; correction: we can help learners become aware of the analytical capability that they already have, probably already use in some realms, so that they can use those skills consciously to solve problems in other realms.
What exactly is analysis? I think it is the making of logical distinctions. Ah, and what is a logical distinction? Depends on the nature of the problem.
One kind of logical distinction is abstract, based on characteristics or qualities we attribute to something. So, for example, we think of Italy as a warm climate, Sweden as a cold climate. Warm and cold - adjectives - are words that describe qualities we attribute to things (in this case, places). So here's a simple analytical problem: Classify the following as warm or cold countries: Mexico, Canada, Norway, Ethiopia, Brazil.
How hard was that? If you can do that, you can analyze. More to come.