Small Sweating Devils and other Inconsistencies

If the devil is in the details.. why are we constantly told not to sweat the small stuff?  I've noticed something about myself.. most of the books that I really enjoy reading are very detailed, including things that seem on the fringe.. but when I try to think in that sense for what I want to write I don't know where and/or what to be detailed on.

For example, a book series I just reread, the Hunger Games, there is a cat that belongs to the younger sister, and the cat plays only a very ancillary part in the story.. it shows the character's personalities and helps illustrate the emotional aspect of both the main character and her younger sister.. but the cat itself has no real part in the stories, only in passing is it mentioned.  Yet the cat is described, in multiple parts of all the books, to some detail.  I get that it's an important part of the younger sister's life.. and that at the conclusion of the series it takes on more meaning.. but it still seems like, in comparison to other things in the series, there is a lot of focus placed on the cat.  I know it serves as multiple roles in the story, both as what it seems and as a measuring stick of the emotional depth of the main character, and a tie to the normalcy of our time..but there are many things that can be used in that regard.  Why the cat?  What makes it special?  That is what kills me.. I can see why it was chosen.. but why was it used in this regard instead of something else?  Why not her father's bow?  Why not the mother's dresses that were worn on Reaping Day?  

I'm afraid that for me, the Devil isn't in the details.. but rather in why those details matter over other details.  I think I'm getting too deep into it and need to step back.. but again, to what level do you step back?  

At what point does this become natural?  Or does it?  Can you learn to identify the proper level of focus, or is that part of the writing process that you're born with, and.. as Stephen King puts it.. "You've either got it or you don't."  

These are the things that cause me to seize up after 10 pages and push the delete button.

**Random Thought of the day**:  "The worst enemy to creativity is self-doubt" -- Sylvia Plath