Aragorn, son of Arathorn, is the last of the line of Isildur. He stands at the foot of a direct male line tracing back six thousand years to the great-great-granddaughter of Elros. He is, in other words, destined to be king.
Or is he? How do we know any of that? The line of Isildur is a secret, known only to the family itself, some few close companions, and the house of Elrond. So... basically it's only Elrond and his relatives who can testify to Aragorn's ancestry beyond, say, two hundred years earlier. The 'line of Isildur' could be a myth, concocted by Elrond when the end of the Third Age seemed to be at hand - a plan devised with a willing Dunadan impersonator, whose son never knew it was a lie.
But maybe that's unfeasible. Surely the Dunedain would have objected. They probably keep records, after all.
And perhaps that's true. But there is another way for Elrond to have raised Aragorn to believe a lie - a far easier way.
In 2930, Arador, Chieftain of the Dunedain (and, we will believe for now, Heir of Isildur) died, leaving his son Arathorn as chief.
In 2931, Arathorn's wife Gilraen had a son, Aragorn.
In 2933, Arathorn was killed by orcs. At this time, a woman arrived in Rivendell with a two-year-old child.
Was she Gilraen? Or was she simply on hand when Gilraen and her son were brutally murdered by orcs? Did this unknown woman, with her own young son, flee to the refuge of Imladris - and, out of desperation and fear, claim to be the one person she knew Elrond would protect: the mother of Isildur's Heir.
We know very little about 'Gilraen', but all of it screams that she was an imposter. She opposed Aragorn's love for Arwen - because she knew that, in truth, he was a peasant, no true match for the 'High Lady'. She stayed in Imladris for many years - because otherwise, she would have met Dunedain who would recognise her, or at least recognise that she was not Gilraen. And when she died, she claimed, "I gave Hope to the Dunedain; I have kept no hope for myself." Yes - she turned her peasant child into the Hope of the Dunedain, but in doing so, her real son had to be erased from history.
Did Elrond know? It's hard to tell. All mortal toddlers probably look alike when you're an immortal Elf Lord, but Elrond bore a Ring of Power. If he knew, why did he keep it a secret? Could it be that he was unable to admit it to himself - unable to accept that the line he had nurtured for thousands of years, his brother's distant descendants, had finally broken?