I'd say it's impossible.
What is possible, at least in my experience, is to start with a good story - i.e. characters, a plot, a series of interesting interconnected events - and let the meaning of those events shine through. I've never managed to craft a story around a message - the message always emerged from the story.
I would say that it's harder to write a great fable or parable than it is to write a great example of a general story, though, because the structure of being built around an Important Point makes it easy to slip into preachiness or didacticism. You have to work extra hard to make the rest of the story not sag under the weight of the lesson.