The immortal soul is a pagan concept. Soul comes from a root word which means to bind. Superstitious pagan peoples would bind the hands and feet upon burial to prevent the dead from harming the living. The word evolved into a similar meaning always associated with large bodies of water (the sea) for the same reason. It was thought that the immortal souls were confined in large bodies of water, preventing them from bothering the living.
When translating the Bible from the Hebrew and Greek to English the word soul would be problematic due to it's pagan roots. However, it was the closest word we had. The Hebrew nephesh and the Greek psykhe are the Biblical terms translated into soul. The Hebrew word comes from a root that literally means "breather." The Greek word has a similar meaning. It means life and all that involves. A living being. That can be somewhat complicated by the usual obstacles, like variation in the the use of the word. Greek philosophers or modern day psychiatrists use the Greek word psykhe corresponds to the Hebrew word nephesh (nefesh, etc.)
The soul, according to the Bible, that is, nephesh or psykhe, is mortal, destructible.
Compare translations Ezekiel 18:4: "Behold, all souls are mine; as the soul of the father, so also the soul of the son is mine: the soul who sins, he shall die." (WEB)
Compare translations Matthew 10:28: "Don't be afraid of those who kill the body, but are not able to kill the soul. Rather, fear him who is able to destroy both soul and body in Gehenna." (WEB)
Journal of Biblical Literature (Vol. XVI, p. 30): "Soul in English usage at the present time conveys usually a very different meaning from נפש [ne′phesh] in Hebrew, and it is easy for the incautious reader to misinterpret."
The New York Times, October 12, 1962: H. M. Orlinsky of Hebrew Union College states regarding nefesh: "Other translators have interpreted it to mean 'soul,' which is completely inaccurate. The Bible does not say we have a soul. 'Nefesh' is the person himself, his need for food, the very blood in his veins, his being."
New Catholic Encyclopedia (1967, V:ol. XIII, p. 467): "Nepes [ne′phesh] is a term of far greater extension than our 'soul,' signifying life (Ex 21.23; Dt 19.21) and its various vital manifestations: breathing (Gn 35.18; Jb 41.13[21]), blood [Gn 9.4; Dt 12.23; Ps 140(141).8], desire (2 Sm 3.21; Prv 23.2). The soul in the O[ld] T[estament] means not a part of man, but the whole man—man as a living being. Similarly, in the N[ew] T[estament] it signifies human life: the life of an individual, conscious subject (Mt 2.20; 6.25; Lk 12.22-23; 14.26; Jn 10.11, 15, 17; 13.37)."
The New American Bible Glossary of Biblical Theology Terms (pp. 27, 28): "In the New Testament, to 'save one's soul' (Mk 8:35) does not mean to save some 'spiritual' part of man, as opposed to his 'body' (in the Platonic sense) but the whole person with emphasis on the fact that the person is living, desiring, loving and willing, etc., in addition to being concrete and physical."
Koehler and Baumgartner's Lexicon in Veteris Testamenti Libros (Leiden, 1958, p. 627) on nephesh: "the breathing substance, making man a[nd] animal living beings Gn 1, 20, the soul (strictly distinct from the greek notion of soul) the seat of which is the blood Gn 9, 4f Lv 17, 11 Dt 12, 23: (249 X) . . . soul = living being, individual, person."
New Catholic Encyclopedia (1967), Vol. XIII, pp. 449, 450: "There is no dichotomy [division] of body and soul in the O[ld] T[estament]. The Israelite saw things concretely, in their totality, and thus he considered men as persons and not as composites. The term nepeš [ne′phesh], though translated by our word soul, never means soul as distinct from the body or the individual person. . . . The term [psy‧khe′] is the N[ew] T[estament] word corresponding with nepeš. It can mean the principle of life, life itself, or the living being."
The New Encyclopædia Britannica (1976), Macropædia, Vol. 15, p. 152: "The Hebrew term for 'soul' (nefesh, that which breathes) was used by Moses . . . , signifying an 'animated being' and applicable equally to nonhuman beings. . . . New Testament usage of psychē ('soul') was comparable to nefesh."
The Jewish Encyclopedia (1910), Vol. VI, p. 564: "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 accordingly nowhere expressly taught in Holy Scripture."
New Catholic Encyclopedia (1967), Vol. XIII, pp. 452, 454: "The Christian concept of a spiritual soul created by God and infused into the body at conception to make man a living whole is the fruit of a long development in Christian philosophy. Only with Origen [died c. 254 C.E.] in the East and St. Augustine [died 430 C.E.] in the West was the soul established as a spiritual substance and a philosophical concept formed of its nature. . . . His [Augustine's] doctrine . . . owed much (including some shortcomings) to Neoplatonism."
Dictionnaire Encyclopédique de la Bible (Valence, France; 1935), edited by Alexandre Westphal, Vol. 2, p. 557: "The concept of immortality is a product of Greek thinking, whereas the hope of a resurrection belongs to Jewish thought. . . . Following Alexander's conquests Judaism gradually absorbed Greek concepts."
The Religion of Babylonia and Assyria (Boston, 1898), M. Jastrow, Jr., p. 556: "The problem of immortality, we have seen, engaged the serious attention of the Babylonian theologians. . . . Neither the people nor the leaders of religious thought ever faced the possibility of the total annihilation of what once was called into existence. Death was a passage to another kind of life."
Plato's "Phaedo," Secs. 64, 105, as published in Great Books of the Western World (1952), edited by R. M. Hutchins, Vol. 7, pp. 223, 245, 246: "Do we believe that there is such a thing as death? . . . Is it not the separation of soul and body? And to be dead is the completion of this; when the soul exists in herself, and is released from the body and the body is released from the soul, what is this but death? . . . And does the soul admit of death? No. Then the soul is immortal? Yes."
Presbyterian Life, May 1, 1970, p. 35: "Immortality of the soul is a Greek notion formed in ancient mystery cults and elaborated by the philosopher Plato."
Phaedo, 80, D, E; 81, A: Plato, quoting Socrates: "The soul, . . . if it departs pure, dragging with it nothing of the body, . . . goes away into that which is like itself, into the invisible, divine, immortal, and wise, and when it arrives there it is happy, freed from error and folly and fear . . . and all the other human ills, and . . . lives in truth through all after time with the gods."
Also see
Liddell and Scott's Greek-English Lexicon, revised by H. Jones, 1968, pp. 2026, 2027;
Donnegan's New Greek and English Lexicon, 1836, p. 1404