There is no inherent meaning to a rose, that doesn't mean that the meanings people have ascribed to it and pull away from it have no value. Humans do this with everything, this shouldn't be an issue when they do it to other human creations as well. Perhaps the author didn't intend for a certain message to come through in their work, but if that's the message a significant amount of people found in it, then that's still warrants discussion, I believe.
I've mentioned this in other threads, but I'm one of those nerds who actually enjoys overanalyzing the art I experience, even if it's a conclusion other people would not have gotten out of it. In fact, I'm a comedian and I'm pretty sure this is the foundation for most comedy - you look at something everyone's familiar with from a different perspective and then you point out, "Hey, this is weird right? It wasn't supposed to be weird, but it's weird, don't you think?"
Even outside of my comedic work (which is the only work I've presented publicly, so far) I find this sort of attitude is valuable to my writing. One of the ways to figure out where your story should go is by determining what the overall theme is; sometimes I get stuck on what happens next in my story and I think to myself "Based on everything that's happened so far, what is my story trying to say? If the message is building up to say X, then maybe the next course of events should enforce that message." Now, like I said, I haven't shared these works of mine yet, so I have no way of confirming whether or not this has been to the benefit of my writing, but I at least feel like it has. Or it's at least helped me get through my "1000 words a day" goal.
And on the topic of English class and how it's taught: all the literature you read in that class will have been curated specifically for this type of teaching. Hamlet didn't get assigned to the syllabus out of random chance - it's been studied for centuries by academics, so there's already a consensus that it's a work that's rife with deeper meanings and symbolism. They ask you to analyze these works because there's so much you could pull out of them that it should come relatively easy. Of course, this leads us to the problem of teachers thinking "Your analysis doesn't match what's in the teacher's handbook, so you fail," but that's just a problem with bad teachers and not the field of literary analysis as a whole.