I recently saw the movie Room 237, which is advertised as a look at the symbolism and hidden messages in Kubrick's The Shining. But what it really is, in my opinion, is a look at seeking hidden messages and symbolism to an absurd degree, filtered through The Shining as an example. The Shining is an excellent vehicle to use for such a thing, since it's filled with lush visuals, and Stanley Kubrick had such a monstrous reputation as a perfectionist. No one would put the same level of hyperanalysis on, say, Michael Bay's Armageddon. What for any other filmmaker would just be considered a continuity error or a happy accident of framing, for Kubrick the presumption is he did it on purpose because he had a message.
Now, I've talked about clarity in writing, but regardless how clear you make things, there will be subtext to be found. It's inevitable, unless your writing is completely devoid of value. Of course, part of that is because we're almost conditioned to look for it, as part of education.
Case in point: probably my favorite "had to read in high school" books was Lord of the Flies. Of the things we were assigned back then it's one of the few that I've gone back and read again just because I wanted to. And because it was a read-for-high-school book, we unpacked loads of subtext. For example, there's the sexual imagery/loss of innocence in the first pig hunt; the id/ego/superego analysis of Jack, Ralph and Piggy; Simon-as-Christ imagery. It's loaded with it. Were all those Golding's intent? Maybe, I don't know. Maybe it's really just about boys going crazy on an island because nothing is stopping them.
But here's the thing, and it's certainly the lesson to take away from Room 237: the analysis of hidden meanings and symbols has far more to do with the analyst* than the artist.
Unless you are one of those deliberate decide-my-subtext-first-and-write-to-it people. Then you're just messing with them.
*- Of all the crackpottery on display in Room 237, I have some real affection for the guy whose core theory is, "The Shining is Kubrick's message of his own feelings of madness and alienation due to his role in faking the moon landing". Because, really, Danny's sweater alone is enough to feed that guy.