How did the Romans tell their story about the twins Romulus and Remus and why did they tell it?

The story of Romulus and Remus was part of the mythical foundation history of Rome. It was therefore recounted in history books as part of chronologically ordered accounts of Rome's early histories. It was normally narrated in the third person in a context that emphasized the growth in power of the city and its conflicts with neighboring tribes. As with most foundation myths, the story emphasizes supernatural occurrences as a way of highlighting the city's strong connection to the gods and the way in which the greatness of Rome was ordained and aided by the gods.
The reason why the story was told was to emphasize the greatness of Rome. The lineage that traces the parentage of Romulus and Remus to Aeneas (a Trojan prince) also provides a legendary explanation of and justification for conquests of Carthage and Greece, as well as a pedigree that allows Rome to appropriate Homer and claim a unique cultural heritage, different from that of the Etruscans and Greeks but equally venerable.
The earliest sources for the story were fourth century BC histories no longer extant. The historian Quintus Fabius Pictor also wrote a history of early Rome that contained the story of Romulus and Remus in the second century; while this work is no longer extant, subsequent histories, including those of Livy, Polybius, and Dionysius of Halicarnassus mention and follow Fabius.