I’m curious if you’re a native English speaker.
Usually quotes are used to question something another person or other people say so I would think you’d quote “classics” or “classics of American literature” to question this story actually being a classic as many other people might say.
Putting quotes on the word “the” in this context seems to be for emphasis and I’ve seen this numerous times with non-native speakers.
If you are a native speaker I don’t mean to be rude, I’m just curious.