I think that if the story makes you project a meaning onto it, then it was a successful story! And any meaning you put on it is constrained by the events of the story itself. So the interpretations you get to are actually guided by the plot and characters combined with your personal experience. And since everyone's experience is different, there will be different emotional reactions and ways to see the story.
When I wrote this I only had an emotion to guide me through it, and that was what I wanted to come through