They did not have the strength to fight Sauron
It is made very clear in the Council of Elrond that there does not exist the strength to withhold the power of Sauron. If they were to attempt to keep it in Rivendell, they would be overthrown in time. The relevant quotes are below.
'but Glorfindel, I think, is right. Power to defy our Enemy is not in [...
Within the novel, Faramir tells Frodo and Sam that Boromir has died, and they fill in the gaps around what happened prior to that.
Faramir smiled grimly. ‘Then you would grieve to learn that Boromir is dead?’
They work out that the days match up so that Faramir's vision is from the same day as they left.
‘But the day when you heard it blowing, if your ...
I've covered this in far more detail in another answer as have others, both here and here.
Put simply, when asked whether they accept his kingship, the men of Gondor called out in agreement. This suggests a pretty unanimous acceptance of Aragorn as their king. It is especially important to note that the quote outlines that all the host and all the ...
There’s this quote from The Return of the King:
Then an old wife, Ioreth, the eldest of the women who served in that
house, looking on the fair face of Faramir, wept, for all the people
loved him. And she said: ‘Alas! if he should die. Would that there
were kings in Gondor, as there were once upon a time, they say! For it
is said in old lore: The ...
Elrond didn't believe Rivendell had the strength to resist Sauron.
What power still remains lies with us, here in Imladris, or with Círdan at the Havens, or in Lórien. But have they the strength, have we here the strength to withstand the Enemy, the coming of Sauron at the last, when all else is overthrown?’
‘I have not the strength,’ said Elrond; ‘...
The theme you are referring to is a beautiful allusion to the deceptive and haunting nature of the Ring.
While the orchestra plays C-minor chord, the violin chimes in with a polite and cold "daaaa-duuuumm," but then it reveals that that was a note from a melody in E-minor key (a completely different one) and proceeds with it against the orchestra "da da da ...