My English professor at Old Dominion University used to say that Robert Frost complained, "You squeeze my poetry too much," meaning that all the deep meanings were really not there.
The thing is, they are, though. The writer may not have intended them as the piece was being written, but you can trace thoughts and patterns back through his writing and find patterns, and argue a meaning of those patterns.
I love literary analysis. It's such an exercise in critical thinking, and it can range from as basic as the word choice, the nuts and bolts of the composition, to the ideas and how they interplay, what allusions are made for what reasons, what symbols are created -- so many ways to approach it, and so much to bring to light (if you're lucky).