Most things were still brand-new in ancient times. As a result, they hadn't become established in the ways they are now—as far as literature went, the earliest Greek writers didn't even have the benefit of distinctions between "tragedy" and "comedy." Granted, that issue was worked out pretty quickly, but the way the ancients thought about literature is instructive to our over-analytical Western mindset: for them it was a unity, simply a body of writing that had to be evaluated work-by-work. They didn't stress over genre labels the way we do.
Sure, they had poetry and drama and philosophy, but even those were pretty fluid boundaries. Is the biblical book of Genesis, for instance, primarily a work of theology, poetry, or historical narrative? Is The Aeneid a poetic epic, or is it a political tract defending the claim of Caesar to the throne? Is Plato's republic primarily artistic or philosophical in scope? And what on earth is The Epic of Gilgamesh (other than one of the greatest works ever penned by the hand of man, of course)?
Mankind figured out the benefit of writing things down pretty early, especially considering there are still societies today without a native written language. We should be glad they did—writing ennabled them to freeze ideas, historical events, people, geography and culture in time, so that we can see in what ways the human race has changed and in what ways we've remained the same (most of them).
Humanists, especially post-Enlightenment, are wont to describe man's progress from a benighted cromagnon to an increasingly sophisticated scientific being capable of improving the world through innovation, education and his own innate goodness. A careful (probably even a cursory) reading of ancient texts will thoroughly belie these claims, and it won't take too long. Evolutionary theories existed at least as far back as the Classical-era Greeks, and probably before; atomic theory began with them as well; and the ancient Egyptians were doing successful brain surgery.
Granted, we know more about the nature of atoms than Democritus did, and evolutionary theory has become increasingly elaborate (and, we may add, ridiculous), but they aren't wholly new ideas. Progress is the white-knuckle hope of those who've rejected God, and ancient literature helps us prove it by showing our "progress" to be nothing more than the compounding of human error and pride.
Not that things haven't changed, or that history isn't going in a specific direction, but man's attempts to get it there are ultimately futile when not grounded in faith in the God of the Bible. It's interesting to note that great literature is still compared to (and largely inspired by) the ancient classics, including the Bible itself; if man is so upwardly mobile, surely we've produced better works than a bunch of sandal-wearing Hellenes and Near Easterners.
Or Chinese Mandarins, or Japanese mystics, or North African mathemeticians, or what have you. Ancient literature doesn't begin and end in Mediterranean cultures. The fact that Westerners have only recently been introduced to Eastern literature doesn't mean it hasn't enjoyed just as long (in some cases, longer) and just as rich a tradition. Whether it's Sun Tzu or Gautama Buddha or Confucius, the Far East has a significant history of thought and literature we would do well to become familiar with.
Understanding today's literature is basically impossible without understanding the literature that preceded it, all the way back to the first forays into essay-writing, philosophy, poetry, etc. Nothing is conceived in a vacuum. Not only the literature of our contemporaries, but also the political, theological and philosophical ideas that inform our world can only be understood and analyzed if we first know our past—these books represent a significant source of such knowledge.