The question of whether the Iliad, especially, and the Odyssey can be traced back to 2000 BCE is a more interesting proposition, and a place where the author seems to be overstating his case. Here’s how he summarizes it:
My claim is that the poems, especially The Iliad, have their beginnings around 2000 B.C.—about 1,000 or 1,200 years earlier than most people say Homer existed. The reason I say that has two strands to it. One is that there are large elements of the Homeric stories, particularly The Iliad, that are shared among the Indo-European world as a whole, all the way from north India through Greece to Germanic and Icelandic stories. There are deep elements in Homer that have nothing to do with Greece or the Aegean.
The second thing is that the situation in The Iliad is very clearly not one in which two deeply civilized nations are opposed to each other. The civilized nation in The Iliad is Troy. It's a well-set-up, organized city, where women lead very dignified lives.
The first claim, that the Homeric poems contain Indo-European elements, is undoubtedly true. The parallels between the Mahabharata and the Iliad have long been noted, and it is not controversial to suspect that behind such similarities is an older set of myths about the wars of the gods, stories later visited on mortals. A clear parallel to the process can be seen in the widespread distribution of the Indo-European serpent-slaying myth, which has reflexed across the Indo-European world. However, can it really be said that the motif of St. George slaying the dragon, one of the latest adaptations of a very old story, means that St. George “originated” in 2500 or 3000 BCE when the serpent-slaying motif likely emerged? It would seem quite odd to argue that the story of St. George existed before Christianity, even if the elements of the story that were folded into his legend came from earlier sources.
In my own book on a similar subject, Jason and the Argonauts through the Ages, I trace elements of the Argonauts story back not just to Mycenaean times but also to the Ancient Near East. The great Classicist M. L. West, amplifying on earlier work done by several German scholars of past centuries, noted that Homer’s Odyssey incorporates and revises elements drawn from an ancient version of the Argonautica, and these in turn seem to draw on elements of Mesopotamian lore, including the Epic of Gilgamesh. (Nicholson is silent on this influence on Homer.) Would we therefore conclude that the Argonautica “originates” in 1900 or 2000 BCE in Mesopotamia? Of course not. It isn’t even a product of Mycenaean Greece, but rather came together in the sub-Mycenaean era from material present in Mycenaean mythology. In my analysis, the core story of Jason and the dragon was likely Mycenaean, with the sea voyage gradually built up during the Dark Age and the Archaic period by oral tradition.
This leads us to the question of the Iliad and the Odyssey. I frankly don’t see what is so deeply impossible about the Iliad reflecting the barbarous, semi-civilized state of Greece during the Mycenaean collapse and the Dark Age. The people of the Iliad are clearly meant to be Mycenaeans. They have Mycenaean social organization, Mycenaean political titles (anax in the Iliad, reflecting the wanax of the Mycenaeans, after the digamma dropped out of Greek), Mycenaean armor (the famous boar’s tusk helmet, which archaeology found), and Mycenaean holdovers in the Greek used in the poems, where some lines are imperfect because of the loss of the digamma (w) between Mycenaean and later Greek. Into this mix are anachronisms—but of later, not earlier, vintage, reflecting the Archaic milieu in which the poems were set down.
Confirmation of this comes from the Hittite texts, from the thirteenth century BCE, which record the existence of Wilusa (Ilion, Troy) and its kind Alaksandu (Alexander; i.e., Paris), and conflicts with the Ahhiya (Achaeans, or Mycenaeans). Nicolson considers this all to be “late” material added to a preexisting epic. But the evidence better fits the idea that the Iliad records a distorted memory of the Mycenaean collapse, the last days of the old system of palaces, international warfare, and grand campaigns, and onto this historical bases old Indo-European myths became folded in, must the way Jason and Odysseus folded old, once-independent stories into the frameworks of their myths.
What I find strange is Nicolson’s measure of how to judge when the Greeks were “civilized” or “uncivilized.” Twice in his interview he gives the role of women as the measure of the poem’s age, going so far as to say that he found it difficult to read Homer because of its lack of well-developed female characters: “it wasn’t easy to spend a few years writing a book about Homer, because it basically shuts you out from the female world.” For Nicolson, the respect (“lives of dignity”) afforded women in Troy and the lack of it in the Greek camp tells him that the story is from the age of barbarism. But that isn’t the case; the Greeks were misogynistic throughout their culture, and it was a truism that the Greeks thought that the truest and greatest love could only exist between equals, that is, two men; Greek mythology depicted the primeval paradise as an all-male world, ruined by the appearance of the first woman.
I don’t see anything in Homer that would suggest that the stories date back to 2000 BCE, at least not in anything like their entirety. To say that elements date back that far is, essentially, to say nothing—it would be like arguing that James Joyce’s Ulysses actually “originates” in Archaic Greece because it reuses and reacts to the skeleton of the Odyssey.
That said, by all accounts Nicolson has written an enjoyable and stimulating book, and I will have to add it to my list of things to read.