This is all well and good, really -- I love 'the classics' to whatever extent that's an agreed upon list (Harold Bloom's the Western Canon (1994), probably its most explicit recent defense, had a list of essential books that was highly controversial and admittedly personal). But I'm concerned that not enough people here have heard the counter-arguments.
The problem is that time is not an unbiased filter, and all the processes of history that anoint and preserve Great Books are not purely a result of their innate or universal value. It's the same argument that's been made for the last 30-40 years about historical archives: what gets saved and how inherently excludes other stories, perspectives, and lives that we're now trying to recover. Often those exclusions are made along lines of power--race, class, gender, etc.
"The Classics" is an idea with its own history that scholars can trace, where the key players are rarely literary critics or sales numbers but institutions (churches, schools, etc.) aligned with powerful interests. Of course it's more complicated, and you'd ideally want to trace each work or groups of texts individually to see how they were 'canonized' and what that meant--but what's important to question is why many of us take this notion of 'the classics' for granted, and whether we might just be stooges of old historical prejudices (that are not, of course, gone). Understandably any effort at 'canonization' makes people nervous, because we'd immediately want to know who's making the decisions.
None of which is reason not to read things considered classic--Tolstoy and Thucydides and Shakespeare are some of my favorite shit-- but to treat the concept with skepticism, appreciate new work that challenges it, and consider each work on its own, rather than as part of some grand corpus handed down from above. It's an attitude that arouses a lot of contempt (Bloom called critics the 'School of Resentment' intent on subjugating all aesthetics to Marxist politcs), but it's really I think just a standard liberal challenge to established authority. In some sense it's a broader playing out of the Reformation rejection of Catholicism's stranglehold on biblical reading and interpretation, except what we're dealing with is the secular equivalent (Great Books). Inevitably there's a radical segment which will call for abandoning these books altogether as vehicles for oppression and nothing more. And every time there's a threat to established church order, including the Reformation, authorities have cried 'antinomianism' (no laws, faith justifies all)--true in a few cases, but misrepresenting the movement as a whole and disqualifying its legitimate criticisms.
Anyway, contemporary writers and publishers are becoming aware of these issues and some have tried to resurrect the lost narratives excluded or unrecognized by 'the Classics,' documenting facets of the human experience that rarely earned entry. Since more people can read and think freely now than ever could during the formation of the Canon, and a lot of these people would not have had a seat at the table if they were alive then, the skepticism of 'Classics' and embrace of modern writers speaking directly to them, makes total sense. The "rich white men" point is a bit overplayed, and often misapplied, but in general it pretty succinctly nails the problem.
tl;dr: there are absolutely great books considered classics but 'the classics' itself is a historical construct that's often been wielded by the powerful for their own ends; lots of folks feel no obligation to it and prefer instead to find modern writers creating new ways forward.