Truth About Death

Religious leaders admit that the doctrine of inherent soul immortality is not in the bible

Jewish Source:
"The belief that the soul continues its existence after the dissolution of the body is a matter of philosophical or theological speculation rather than of  simple faith, and is nowhere expressly taught in Holy Scripture.
Jewish Encyclopedia

Justin Martyr:

"For I choose to follow not men or men's doctrines, but God and the doctrines [delivered] by Him. For if you have fallen in with some who are called Christians, but who do not admit this [truth], and venture to blaspheme the God of Abraham, and the God of Isaac, and the God of Jacob ; who say there is no resurrection of the dead, and that their souls, when they die, are taken to heaven; do not imagine that they are Christians." Dialogue of Justin, p. 460

Tatian of Assyria

“The soul is not in itself immortal, O Greeks, but mortal.”

Address of Titian to the Greeks

Theophilus of Antioch

“But someone will say to us, Was man made by nature mortal? Certainly not. Was he, then, immortal? Neither do we affirm this. But one will say, Was he, then, Nothing? Not even this hits the mark. He was by nature neither mortal nor immortal. For, if He had made him immortal from the beginning, He would have made him God. Again, if He had made him mortal, God would seem to be the cause of his death. Neither, then, immortal, nor yet mortal, did He make him, but, as we have said above, capable of both; so that if he should incline to the things of immortality, keeping the commandment of God, he should receive as reward from Him immortality, and should become [as] God [is]; but if, on the other hand, he should turn to the things of death, disobeying God, he should himself be the cause of death to himself.” The Ante-Nicene fathers

Catholic Source:

"The immortality of the human soul is one of the fundamental tenant of the Christian religion... Catholic philosophers, however, with the exception of Scotus and his followers, have generally claimed to establish the validity of the belief apart from revelation. The Catholic Encyclopedia 

William Tyndale:

"And ye, in putting them [the departed souls] in heaven, hell and purgatory, destroy the arguments wherewith Christ and Paul prove the resurrection...And again, if the souls be in heaven, tell me why they be not in as good a case as the angels be? And then what cause is there of the resurrection?" 

— William Tyndale, An Answer to Sir Thomas More's Dialogue (1530) 
 
Martin Luther:
Luther placed the dogma of the immortality of the soul among the " monstrous fables that form part of the Roman dunghill of decretals."
 
"Salomon judgeth that the dead are a sleepe, and feele nothing at all. For the dead lye there accompting neyther dayes nor yeares, but when they are awoken, they shall seeme to have slept scarce one minute." 
— Martin Luther, An Exposition of Salomon's Booke, called Ecclesiastes or the Preacher (translation 1573).

Anglican Source:

"'The Immortality of the Soul' is a doctrine of Heathen Origin...The doctrine of the existence of the soul or spirit of man in happiness or misery after death, independent of the body, is nowhere found in the Old or New Testament Scriptures" (George Waller, The Biblical View of the Soul, p. 65)
The quotations can be found online in google books here and here

Presbyterian Sources:
"The immortality of the soul, and a future state, after we believe a God, we may be persuaded of these from Divine revelation ; and that doth give us the highest and firmest assurance of them in the resurrection of Christ from the dead. Yet I do not find but that these also are rather supposed, than expressly revealed, in the Bible." Works by John Tillotson

"...it was through the Platonists that the true Greek doctrine of the soul was passed on to Christian theology." Encyclopedia of Religion and Ethics

"Man is not a dichotomy, half mortal and half immortal, but a being whose total psychosomatic existence is at every moment dependent upon God"
(Dr. James J. Heller,  Theology Today, XV, July 1958. p. 222)

Evangelical Source: 

“Speculation about the soul in the subapostolic church was heavily influenced by Greek philosophy. This is seen in Origen’s acceptance of Plato’s doctrine of the preexistence of the soul as pure mind...” The Evangelical Dictionary of Theology

 C.S.Lewis on hell:

"But I notice that Our Lord, while stressing the terror of hell with unsparing severity usually emphasizes the idea not of duration but of finality. Consignment to the destroying fire is usually treated as the end of the story —not as the beginning of a new story. That the lost soul is eternally fixed in its diabolical attitude we cannot doubt: but whether this eternal fixity implies endless duration—or duration at all— we cannot say.“ The Problem of Pain, p. 129

Others who affirm conditional soul immortality:

John Milton, Thomas Hobbes, Richard Overton, Isaac Newton, The Adventists, etc.