nobodysuspectsthebutterfly:

The Gift of Men is that when they die, they are freed from the world, whereas Elves are always bound to it. Elves must live as long as the world exists and are burdened with its sorrows, but Men are freed from this destiny, with a fate that only Elu Iluvatar knows.

The point? It’s probably something Catholic. Athrabeth Finrod ah Andreth (published in HoME vol 10, Morgoth’s Ring, which has a ton of Tolkien’s metaphysical and philosophical worldbuilding*), is a discussion that took place during the First Age between the Elf Finrod Felagund and the Man (woman) Andreth, Finrod’s brother’s would-have-been lover. The conversation, which Tolkien intended to include in the Silmarillion, revolves around the Elvish and Man beliefs about death, including how Men no longer view it as a gift but rather a doom, and believe it is a corruption, their punishment for being tempted to worship Morgoth. (cf original sin.)

*(For example, “Morgoth’s Ring” is the world, because he changed it so
much that he put his essence and power into it, like Sauron did with the Ring.
There is a fundamental marring of the world because of Morgoth, in the land and in its people, and only
when it is destroyed and recreated will it become the perfect world the
Eru intended it to be. For another example, see the nature of Orcs.)

Andreth goes on to describe those of her people who hold to the Old Hope, that one day Eru himself will enter into the world and heal Men from the marring.

‘Are you then nor one of them?’
‘How can I be, lord? All wisdom is against them. Who is the One, whom ye call Eru? […] How could Eru enter into the thing that He has made, and than which He is beyond measure greater? Can the singer enter into his tale or the designer into his picture?’
‘He is already in it, as well as outside,’ said Finrod. ‘But indeed the “in-dwelling” and the “out-living” are not in the same mode.’
‘Truly,’ said Andreth. ‘So may Eru in that mode be present in Ea that proceeded from Him. But they speak of Eru Himself entering into Arda, and that is a thing wholly different. How could He the greater do this? Would it not shatter Arda, or indeed all Ea?’
‘Ask me not,’ said Finrod. ‘These things are beyond the compass of the wisdom of the Eldar, or of the Valar maybe. But I doubt that our words may mislead us, and that when you say “greater” you think of the dimensions of Arda, in which the greater vessel may not be contained in the less. But such words may not be used of the Measureless. If Eru wished to do this, I do not doubt that He would find a way, though I cannot foresee it. For, as it seems to me, even if He in Himself were to enter in, He must still remain also as He is: the Author without.’
[…] ‘Then, lord,’ said Andreth, and she looked up in wonder, ‘you believe in this Hope?’
‘Ask me not yet,’ he answered. ‘For it is still to me but strange news that comes from afar.’

This is very much a Jesus reference, and sooooo Catholic. Tolkien generally eschewed allegory (he thought C.S. Lewis was basically trying way too hard with Narnia), but per one of his letters, he said “The Lord of the Rings is of course a fundamentally religious and
Catholic work, unconsciously so at first, but consciously in the
revision.”
The main books are subtle, but his notes (unpublished in his lifetime) far less so.

Though if we step away from the Catholicism, there’s another belief of Finrod’s that may apply here. Quoting the wiki’s summary:

Men were not the ‘followers’ of the Firstborn but the heirs of Arda, who
will heal the Marring of Arda and enlarge the Music to surpass the
Vision of the World.
In this way, the Eldar may be saved from their own death, which was
inevitable with the ending of Arda. Through the fulfilment of the errand
of the Second Children,
they will be restored. And he has a fair vision of the Eldar and Men
dwelling in the beautiful, green world together. The Eldar would then
sing to Men of all that had been from the beginning. The world remade
would be the true home of Men’s spirit, with their fëar and hröa
united, and it would then be the Eldar who, unchanged, remembered and
spoke of the world that had been to teach the love of it to Men. The Eldar’s burden of memory, which weighed down their spirit in life, would become their wealth in the Days to come. 

So the point of the different fates of Men and Elves is that each will have a different role in the future Arda Remade. Men and the spirits of Men (returned from wherever Eru has sent them), will heal the world and make it perfect as it should be, even greater than Eru’s original vision. And there Elves, the keepers of the history of the world, will share all that they know with Men.

Anyway, there’s far more to the discussion, all about the nature of death and the fear that comes with it, for both Men and Elves. And then Tolkien comments on it, and Christopher Tolkien comments on it, it does go on. It’s extremely metaphysical, too much for me to discuss here without pages of quotes, and I’m not even sure I fully understand it myself. There may be academic essays elsewhere on the internet (with Tolkien fandom, of course there is), but I suggest reading the Athrabeth yourself to start. (Libraries often have copies of the History of Middle Earth, among other ways of acquiring them.) Still, I hope that what I have here helps, a little bit at least…