I think it's implied that some Elves show cognitive dissonance towards the Gift of Men. It's said on this page, emphasis mine:
But as the years grow long and Time wears, even the Valar will come to envy the gift of Ilúvatar to the race of Men, that of liberation from the physical world, and the inevitability of loss and sorrows that must come with this existence within Arda.
I think this is implying even the Valar, as in, Elves included, envy the fact that the spirits of men are removed from the world and return to rest with Eru, beyond even their own comprehension. It's easy to attack something you can't understand, especially when you feel like you might be missing out on something special.
My understanding is it is because of this envy, that Elves sometimes show bitterness towards the race of Men, who get to rest with the big man upstairs when all is said and done. Elves, meanwhile have to sit in the Halls of Mandos until the end of the world, and twiddle their thumbs.