The Trojans were losers, but they were very heroic losers. While there are readings of the Iliad that paint the Trojans in a somewhat negative light, I think the most natural readings, and those supported most by later authors, give the Trojans a great deal of glory. And this glorification of a heroic defeat is hardly unique to the Romans--in the debates over English historical identity, for example, the defeated Anglo Saxons won out over the Norman conquerors, and there are rather more statues of Boudicca in Britain than of Suetonius Paulinus.

But beyond that, the deeper question is "why the Trojan War?" After all the Romans were not Greeks, so why wrap so much identity up in a Greek poem? The answer to this goes back quite a bit farther than the conquest of Greece. During early Greek colonization of the western Mediterranean, Greek cultural products became very popular within Italy. For example, one of the most iconic Greek artistic products are the black figure vases, but the great majority of these have actually been found in Italy, and were originally thought to be created by the Etruscans. This importation of material also included an importation of ideas, and in particular Odysseus became a popular founding figure among many of the Etruscan settlements. The Roman adoption of Aeneas is within this Italian context in which the "Greek" figures of the Trojan War became heroic figures within Italian communities.

A classic study of the way ethnicity and heroic stories became entangled is The Returns of Odysseus, although it is largely from the Greek perspective.

(Similar-ish) Piggyback question- Why would Snorri Sturluson claim [Edit- or perhaps a better word would be "portray"] that the Norse gods were from Troy/Anatolia in the Prose Edda? Would he have known about the legendary origins of Rome?

The short answer is that the Trojans weren't depicted as losers in the literature of the day, or even in the Illiad. Virgil's "Aeneid," which makes much of the Trojan connection, was actually commissioned by Emperor Augustus specifically to make Rome's foundation story more noble. In it the Trojans are depicted as immensely honourable, even the aged King Prius straps on his armour in a last stand, and is mowed down by treacherous and deceitful invaders.

They are also depicted as falling for a trick that any pious person would fall for under the circumstances, and piousness is a significant theme in the epic, one emphasized in Aeneas in particular. This is because this is a trait Augustus hoped to cultivate in the modern day populace. When Laocoon, a priest, tries to reveal the trickery behind the Trojan Horse, he and his sons are devoured by a sea monster. Under such circumstances, well, any god fearing upright citizen is going to be taking that horse into the city stat. A lot of effort is also put in to excusing Aeneas for running as Troy fell, Venus tells him to go and he has dreams, all pointing to the fact that the founding of Rome is his destiny, it is preordained.

So apart from wanting a bit of Greek ancestry and that connection to antiquity, as /u/Tiako notes, you'll also see that in the commissioned origin story of Rome, the Trojans are by no means depicted as losers. I mean even in the Illiad Homer has a lot of respect for Hector (the next in line for the throne), but absolutely none for Paris (Hector's younger, flashier but more cowardly, brother) mind you. All in all, in "The Iliiad," Hector is depicted as very noble. Edit: Even the gods intervene after Achilles has dragged Hector's dead body around for a few days behind his chariot, so that the Trojan's body can be returned to his father for a proper burial.

The reason for all of this revisionist history, moreover, is because the history that Livy had been producing wasn't producing particularly noble results. I mean you had Romulus and Remus fighting to the death (two boys literally raised by wolves no less), the Rape of the Sabine women (the ruse to populate Rome by kidnapping their neighbours' wives), the Rape of Lucretia, you name it. Overall, Rome's founders were coming out looking like a bunch of savages. Given all this, if Troy had a particularly bad rap among Romans, Augustus never would have green-lit it as the place of origin. And really, why would they have a negative view? We're talking about a city that got suckered into a war because their Prince couldn't keep it in his pants. In spite of this, they withstood opposing forces for 10 years, so even in the Illiad we see them putting up a helluva good fight and doing so until the bitter end.

Everyone here seems to be assuming that Romans were not actually descendants of Trojans, or could not have known that. Couldn't the myth have had more than a little basis in fact? Couldn't their origin myths have been based on their actual origin?

A follow up question: did Virgil invent the notion that Romans were descendants from Trojans or did he expand on an already existing myth?

This question may have been answered here already:

https://www.reddit.com/r/AskHistorians/comments/35uy9l/why_would_the_romans_have_wanted_to_view/

/u/publiusclodius

It's easy for us to look at the Greeks as being the heroes of the Trojan War, but that's not necessarily how the Romans would have viewed them. The Greeks may have won the war, but they did so through a clever trick: the Trojan horse. The legend of the horse appeals to our modern sensibilities as a strategic parable, but perhaps not so to honor-obsessed ancient Romans.

Livy, in his History of Rome, quotes Roman senators as saying "Our ancestors did not conduct their wars by lurking in ambush and attacking by night, nor by feigning flight and then turning back unexpectedly upon the enemy when he was off guard, and they did not pride themselves on cunning more than on true valor . . . This is the Roman scrupulousness, unlike the cunning of the Carthaginians or the cleverness of the Greeks, who pride themselves more on deceiving an enemy than on overcoming him by force." (Roman Civilization Vol. I, ed. Naphtali Lewis & Meyer Reinhold; 3rd Ed. pg 203)

Conservative Romans were also wary and distrustful of Greek culture, another potential reason why they would not identify themselves with the Greeks of the Trojan War. Of Cato the Elder, Plutarch writes "Out of a patriotic zeal [he] mocked all Greek culture and learning . . . He declared, as it were with the voice of a prophet or seer, that the Romans would lose their empire when they began to be infected with Greek literature." (Roman Civilization Vol. I, pg 529).

Another thing to keep in mind is that Troy, as the legend goes, was a prosperous, regional super-power that was attacked by a confederation of angry Greek tribes. I think it makes sense that the Romans, always spooked by the lingering terrors of the Gallic sack of Rome, would (perhaps ironically) identify more with Troy under siege than with the invading Greeks.

It may be behind a pay-wall, but this very recent (15 June 17) London Review article is directly of interest. A review of "Virgil’s Ascanius: Imagining the Future in the ‘Aeneid’ by Anne Rogerson, it focuses on the SON of Aeneas, and adds a lot of interest to what others have written already. Dennis Feeney notes that the Romans, for ended up adopting what was initially a story to help the Greeks make sense of the world in order to link themselves into a wider and older cultural tradition. It's a story which evolved over time, with Virgil modifying and altering it. More straightforwardly, even though Troy fell, it was heroic in defeat, so is good to mine for prestige because of Aeneas' alleged involvement in an unbroken chain leading to the founding of Rome, via Alba Longa: (earlier versions of the story have Rome being founded far sooner than it could have been after Troy)

https://www.lrb.co.uk/v39/n12/denis-feeney/between-troy-and-rome

Worth seeking out the whole thing, but I've snipped a few of the most interesting parts relating to the Roman/Trojan identity links:

When Troy fell to the Greeks, the story goes, Aeneas, the son of Venus and Anchises, survived and escaped from the burning city with his father and young son Ascanius (also called Iulus). After years of wandering, the Trojans reached Italy and settled in Latium, where Aeneas married the Latin princess Lavinia and founded a city named Lavinium after her. Following the death of Aeneas, Ascanius established a new city, Alba Longa, and a long line of Alban kings eventually resulted in the birth of the twins Romulus and Remus, who founded the city of Rome, hundreds of years after the Trojans’ arrival in Italy.... Trojan glamour was a powerful asset in the competitive world of the Roman nobility, and many families played the inheritance game – so many that two scholars, Varro and Hyginus, wrote books On the Trojan Families. There were other lineages of note, too: many Roman families claimed to have non-Trojan heroes and demigods in their ancestry

For political reasons, Virgil ends up fudging two versions of the story around Ascanius which feeds into Roman identity:

Such a startling lack of precision at the origin of the Roman people has destabilising implications if we take the Just-So dimension of Virgil’s epic seriously. The Trojan/Latin heir is called Silvius because he was born in the woods (silvae). This is about as natural as you can get, a reversion to the first Latin named in Greek literature, the Agrios (‘Mr Wild Man’) who ruled the Etruscans with his brother Latinos, according to a passage in the Hesiodic corpus, from the second half of the sixth century BCE. The Trojans, on the other hand, as Edith Hall showed almost thirty years ago in Inventing the Barbarian, had stood as a model of oriental hyper-civilisation since the fifth century BCE, when the tragedians of Athens co-opted Homer’s Trojans into the roles of their contemporary Persian enemies. The split tradition of the sons of Aeneas helps to bring into focus a major preoccupation of the epic, which, in order to question the nature of Roman identity in the world of Augustus, engineers a tension between the homegrown naturalness of the Latins and the dangerously effete civilisation imported by the Trojans. Since Augustus had expended a lot of energy painting his rival, Mark Antony, as a decadent debauchee in thrall to an oriental queen, the Trojan inheritance was difficult to embrace wholeheartedly, and the figure of Ascanius, ‘poised between Troy and Rome’, is ‘an important reminder of the ongoing, if troubling, importance of Troy to Augustan Rome’