Why does Aragorn say this about Narsil?

Question

Aragorn is quoted as saying (emphasis mine) :

'For the Sword that was Broken is the Sword of Elendil that broke beneath him when he fell. It has been treasured by his heirs when all other heirlooms were lost; for it was spoken of old among us that it should be made again when the Ring, Isildur's Bane, was found. Now you have seen the sword that you have sought, what would you ask?'
_{The Lord of the Rings: The Fellowship of the Ring : Chapter 2 The Council of Elrond}

But we know from the appendices that many years prior to this Elrond told Aragorn this:

"Here is the ring of Barahir," he said, "the token of our kinship from afar; and here also are the shards of Narsil. With these you may yet do great deeds; for I foretell that the span of your life shall be greater than the measure of Men, unless evil befalls you or you fail at the test. But the test will be hard and long. The Sceptre of Annúminas I withhold, for you have yet to earn it."
_{The Lord of the Rings : Appendix A (v) : Here Follows a Part of The Tale of Aragorn and Arwen}

Why would Aragorn say that all other heirlooms are lost when he knows that others exist?

Answer 1

This isn't directly answered, but I can see two possible explanations:

1. Aragorn is hyperbolizing

2. There's some tense confusion going on.

   Aragorn's statement does not necessarily mean that all other heirlooms are currently lost, just that there was a period, an indeterminate amount of time in the past, where this was the case; it's entirely possible for a lost heirloom to be recovered later, and that sentence still hold true. Another way of expressing the same idea, which may be more clear, would be:

   The sword of Elendil was treasured by his heirs, even in a time when they had no other heirlooms to treasure.

   This is, in fact, believed to have happened with the Ring of Barahir; Arvedui gave a ring to the Lossoth chief in TA 1975, shortly before his (Arvedui's) death:

   [T]he chief of the Lossoth said to Arvedui: "Do not mount on this sea-monster! If they have them, let the seamen bring us food and other things that we need, and you may stay here till the Witch-king goes home. For in summer his power wanes; but now his breath is deadly, and his cold arm is long."

   'But Arvedui did not take his counsel. He thanked him, and at parting gave him his ring, saying: "This is a thing of worth beyond your reckoning. For its ancientry alone. It has no power, save the esteem in which those hold it who love my house. It will not help you, but if ever you are in need, my kin will ransom it with great store of all that you desire."

   ^{Return of the King Appendix A: "Annals of the Kings and Rulers" I: "The Númenórean Kings" (iii) Eriador, Arnor, and the Heirs of Isildur}

   A footnote mentions that this ring is believed to have been the Ring of Barahir, which was recovered later:

   In this way the ring of the House of Isildur was saved; for it was afterwards ransomed by the Dúnedain. It is said that it was none other than the ring which Felagund of Nargothrond gave to Barahir, and Beren recovered at great peril.

   ^{Return of the King Appendix A: "Annals of the Kings and Rulers" I: "The Númenórean Kings" (iii) Eriador, Arnor, and the Heirs of Isildur}

   Though the history of the Sceptre of Annúminas isn't well-detailed, considering the contested history of that region I wouldn't be surprised to learn that it had a similarly checkered past