The souls of Mortal Men are in opposition to the Elves and that is why Mankind is not allowed to enter the Blessed Realm.
From the very beginning Mortal Men and any other race besides the Elves and the angelic spirits, the Maiar and the Ainur, were prohibited to enter Aman. This was not instated by the Powers but is bound in the nature of Men and in the "Doom" of Eru: the difference of his children and the speed of their growth, their lifespan and the nature and fate of their souls. Even if the Valar desired to open up their realm for Mortal men they could not. It was forbidden by Eru, as the Powers told the Nùmenòreans, and only he could grant the gift of immortality to Men.
The Elves were in origin of souls very much like the Powers; their souls were created to stay within the time of Arda and only cease to exist or "die" when the time measured for Arda ran out. But the souls of Men were not bound within the time of Arda and the span of time granted to their souls was the same length as that of their body; whereas the bodies of the Elves if destroyed had the possibility to rehouse the soul anew.
Time in Aman was of a different kind: time did not run as fast as in the Mortal lands. One year in Aman was as much as 9,582 years in the Mortal lands, so the lifespan of a man in the Blessed realm would only last ten years in Aman. This means that the body of a Man would wither and die when it was ten years and his soul, also ten years old and just beginning to encounter the joy of the world, would die with it or try to cling to the aged and dying body with pain and agony.
If we assume that the body of a Man in Aman where no grief or sickness would assail it could live on, enjoying the bodily living, what then of the soul bound within the body ? The nature of the human soul would prevent the joyful life in Aman. The soul of a man was designed to stay in time for only so long and soon it would begin to long for the release of the body and go to where Human souls have to go. That would mean death to the body too or, if the flesh were the stronger, to hold the soul back with the same result.
The truth of this is seen in the history of the Nùmenòrians who were granted a triple (and then some) lifespan. In the beginning when they still believed and held Eru and the Valar in honour they freely laid themselves down to die when either soul or body was weary of life. At that time they lived in joy and harmony and were not afraid of death; it was the natural end of a period. After the coming of the Shadow they began to hunger for immortality and fear the death. Their lives were shortened and death became a horror to them, an evil ending, with pain and a forced divorcing between the former united body and soul.
References: Morgoth`s Ring, Silmarillion