Many people think that one of the important things English courses and
English teachers do is make sure everybody's read "the great texts," or
at least been in the room while a discussion of them was carried on.
So people assume that an English course will be on in which someone will
tell them what the "great texts" are (and they'll be Shakespeare, some
nineteenth century novels, and some Romantic and sixteenth century poetry).
I don't think this is the central issue: I think the central issue to to help people become the sort of person who actually cares about that sort of literature, and might read it later in life, go to plays, and generally engage herself with writing as an art form. I'm not sure the best way to do that is to take a list of "great works" and do the English course thing with them. I think a much better way is to create a situation in which people have a chance to get better at attending to texts, and to written (and oral) language, and to deepen their awareness of how it works. If at the end of that they're better readers and writers (and listeners and speakers) I think that's far more important than whether they know some plots from Shakespeare, some good lines from poetry, and some opening lines from great novels.
Not only that, the English department agrees with me (or at least they've said publicly they agree with me). If you check out their statement on goals for English 1006, you'll see there's not a word there about the history of literature, Shakespeare, or great novels.