In the Return of The King, we see that Elrond doesn't seem so enthusiastic to re-forge the sword. Why is that?
In this scene, Elrond shows why:
In text, the relevant conversation is as follows:
Elrond: "The time of the Elves is over, my people are leaving these shores. Who will you look to when we've gone? The Dwarves? They hide in their mountains seeking riches, they care nothing for the troubles of others."
Gandalf: "It is in Men that we must place our hope."
Elrond: "Men? Men are weak. The race of Men is failing. The blood of Numenor is all but spent, its pride and dignity forgotten. It is because of Men the Ring survives. I was there Gandalf. I was there three thousand years ago, when Isildur took the Ring. I was there the day the strength of Men failed."
[flashback of that day]
Elrond: "It should've ended that day, but evil was allowed to endure. Isildur kept the Ring. The line of kings is broken. There is no strength left in the world of Men. They're scattered, divided, leaderless."
Gandalf: "There is one who could unite them, one who could reclaim the throne of Gondor."
Elrond: "He turned from that path long time ago. He has chosen exile."
This conversation shows exactly why he refuses to reforge Narsil, the blade of the Númenórean king of Gondor:
- To Elrond, the bloodline of Númenor is spent and gone.
- Aragorn is a rightful heir to the throne of Gondor by his Númenórean blood, and Elrond knows it.
- However, the nobility of the line has failed the day it succumbed to the temptation of the One Ring. Aragorn has also chosen to be a Ranger, not who he was born to be. As such, he considers Aragorn unworthy of his lineage.
- As such, there is no meaning and nobody to reforge the blade for, least of all that Ranger guy.
- At this point, Elrond is looking upon Middle-earth and thinking:
That is why he rejects Arwen's pleas at the start:
To Elrond, Arwen's request is nothing more than a desperate plea for her lover, a futile endeavour considering Aragorn's perceived unworthiness to wield the blade of the king, and the weakness of his blood before the might of Sauron.
It is only when he realised that Arwen has chosen the mortal life of Man, that there is no more ship that can bear her west to Valinor, that his daughter's fate is now tied to the fate of Middle-earth, that he finally decided to reforge the sword (and set out to persuade Aragorn to put aside the Ranger).
Elrond didn't reforge the sword because his faith in humanity was restored. He reforged it because doing something, however futile, is better than doing nothing when it comes to saving his own child's life.
If I have one beef with Peter Jackson's films, it's how hard he tried to create added tension that didn't exist in the books. It may seem trivial, but to me it very much undermines a huge theme in the books, which is the solidarity and resolution the Free People of Middle-earth felt when confronted by the Shadow. In the books, Theoden never once considered not going to Gondor's aid, nor did he express resentment towards them for not aiding him in battle (I assume he understood the fact that Gondor had it's own problems to worry about being next-door neighbors with Sauron). Treebeard was never opposed to assailing Isengard. Faramir understood the peril of the Ring from the start and made it expressly clear that he would under no circumstances take the Ring for Gondor's use. And, lastly, Elrond was not against the re-forging of Narsil. In fact, he was the one encouraging Aragorn to step up and take the title given to him. Although, Aragorn was not as hesitant to do this as he was in the films either.
There's a lot more nobility, honor, and valor in the books, a lot of which being due to racial traits among the characters (Elf-blood, Númenórean blood, etc.) that P.J. cut out of the picture. To make a rambling comment short; the element in question of Elrond being against the reforging on Narsil was simply a device conceived by the P.J. for dramatic effect. There's really no deeper meaning to be found in it.
As for Elrond's feelings concerning Aragorn's life of exile, it wasn't simply that Aragorn turned away from his destiny and went into hiding as a Ranger. Aragorn was raised in Rivendell by Elrond. The Rangers are the descendants of the Númenóreans - that's what they do: they protect the remnants of their ancestral Homeland. It's understood that all the things prophesied to take place (the Return of the King, the reforging of the sword that was Broken) are to happen when the time is right, which other prophecies alluded to.
And Elrond talking about how the "blood of Númenor is spent, men are weak" etc. He simply wouldn't have actually said such a thing. In many individuals, the blood of Númenor was barely traceable, if there at all. But there were still individuals, such as Aragorn and Faramir, in which the blood of Númenor still ran strong, and Elrond having raised Aragorn would be well aware of that. They also are related and come from the same blood line. They are both descended in long line from Beren and Lúthien. Elrond would never have spoken of the Line of Lúthien failing or being worthless. So again I say, pure Hollywood dramatic effect and nothing more.