The thing is, writing is about communication. I have a story that I want to communicate to other people. If I talk too much about it the urge to write it will diminish. That's the primary reason I shy away from talking about what I do. Better to say nothing.
The second reason for being coy is I write what I write; I can't write it differently because I'm me, not someone else. Whether someone likes what I'm in the process of writing should be irrelevant - yet I know that I will be hugely affected by a disappointed face. It might even put me off writing. Better to say nothing.
The third reason for mumbling is that I dread someone brightly saying, 'Oh, that's just the same story as one I read last week,' or, 'that's just like the plot of Eastenders/the Archers.' I know with my brain that there are no new stories and it's only your take that can possibly be original, but my heart isn't so sensible. It will shrivel up and lose all confidence in the story. Better to say nothing.
Workshopping is different because either it's a whole piece and therefore the story has already been committed to the page, or it's a fragment. Plus, I trust the people I workshop with. I know them, they're all writers and they know how to be critical but supportive at the same time.
Generally I advise all writers to keep their story telling for the page. Don't share with your friends or your partner even if they ask. Let them read it when it's ready to be read by non-writers, and not before. Don't talk - write!