WHY "show, not tell"

I was recently reading a short story that just didn't keep me interested, and I finally figured out why:  the story was full of TELLING details, instead of SHOWING details.  I'm (kinda) paraphrasing here, but the protagonist thinks at one point, "I'm sad that I hurt my wife.  She deserves better."  

Anyone who has ever read a book on the craft of writing or attended a writing conference has likely heard the piece of advice, "show, don't tell."  For instance, the sentence above *could've* been more along the lines of, "Thinking about what I did to her... no!  I can't even think about it.  It makes me sick to my stomach."  We understand through showing details that he feels remorse. 

But why is showing more powerful than telling?  It occurred to me, when I read this story, that no one is so in touch with their emotions that they can pinpoint what they are feeling at any given moment.  In other words, when your spouse leaves a coffee cup half-filled with coffee in his office for three days >ahem!<, you don't think to yourself, "I'm so angry at him!"  No, instead you think, "Honestly?  Does he know where the sink is?"  

Showing is more honest, and honesty in fiction is power.  Showing allows us to *be* the main character, rather than *hear* him/her.  Showing doesn't hit you over the head with an emotion ("I'm sad."), it allows you to feel that emotion.  And nothing rewards your readers more than that.