I think I want to get away from the idea that poetry is a "puzzle." Puzzles have single answers, even if you can't work out what the answer is. So people ask, "what does poem X mean?" as if you can supply them with the answer. And it's not as if you can't supply an answer; you can, if the poem is more than just an exercise. But it's an answer not the answer.
So I often ask, what do you think it means?
And then nod when they tell me.
A poem is not a puzzle. It is a field of meaning, of sounds harmonising and not harmonising, of ideas and feelings and registers of language. It might be univocal or multivocal. It might represent the author's thoughts, but those thoughts might be provisional not fully formed. A poem is a stimulus for the reader's thoughts, not simply a statement of the writer's thoughts.
Some of the greatest literature in the world has been spoiled because readers want nice definite answers to it. The Bible, for instance. People go it it, ask it questions it wasn't designed to answer ("Is abortion wrong?" for instance) and either find exactly what they're looking for or complain when it doesn't do what they think it should. But the Bible - in common with most great literature - was not designed to give answers, but to stimulate thought. The writers of the Bible weren't the systematic theologians of the later church; they were much more unsystematic, working things out as they're going along. That's why I still read it, when I can rid myself of 2000 years worth of theology.
Take the creation narratives, for instance. They weren't intended to be science - no ancient Hebrew would have known scientific method from a hole in their boots - they were stories, intended to be told to hearers in the synagogue and the Temple. Arguing over whether they're scientifically accurate is pointless. The first chapter is a beautifully constructed prose poem, the second chapter is a tale, lovingly retold. They're ancient in origin, and they feel it; but they pose questions about the world such as: where do we come from? Is there a god? Does life have a meaning? 2000 years of theology has spoiled them. I think we need to strip that away and get to the real simplicity of the story underneath.