The Soul is not Immortal Per Se
For God alone is unbegotten and incorruptible, and therefore He is God, but all other things after Him are created and corruptible. For this reason souls both die and are punished: since, if they were unbegotten, they would neither sin, nor be filled with folly, nor be cowardly, and again ferocious; nor would they willingly transform into swine, and serpents, and dogs; and it would not indeed be just to compel them, if they be unbegotten. For that which is unbegotten is similar to, equal to, and the same with that which is unbegotten; and neither in power nor in honour should the one be preferred to the other, and hence there are not many things which are unbegotten: for if there were some difference between them, you would not discover the cause of the difference, though you searched for it; but after letting the mind ever wander to infinity, you would at length, wearied out, take your stand on one Unbegotten, and say that this is the Cause of all.
— Justin Martyr, Dialogue with Trypho, ch. 5
To paraphrase Justin, if many things are uncaused or immortal per se, then what causes the differences or similarities between them? Among others, the immortality which is common to them must necessarily have a cause. But then, if there is a cause of their immortality, they are not uncaused.
Spirit Gives Life, Soul Partakes in Life
Soul assuredly is or has life. If it is life, it would cause something else, and not itself, to live, even as motion would move something else than itself. But if it lives, it lives not as being life, but as the partaker of life; but that which partakes of anything, is different from that of which it does partake. Soul partakes of life, since God wills it to live. Thus, then, it will not even partake [of life] when God does not will it to live. For to live is not its attribute, as it is God’s; but as a man does not live always, and the soul is not for ever conjoined with the body, since, whenever this harmony must be broken up, the soul leaves the body, and the man exists no longer; even so, whenever the soul must cease to exist, the spirit of life is removed from it, and there is no more soul, but it goes back to the place from whence it was taken.
— Justin Martyr, Dialogue with Trypho, ch. 6
As the animal body is certainly not itself the soul, yet has fellowship with the soul as long as God pleases; so the soul herself is not life, but partakes in that life bestowed upon her by God. Wherefore also the prophetic word declares of the first-formed man, “He became a living soul,” teaching us that by the participation of life the soul became alive; so that the soul, and the life which it possesses, must be understood as being separate existences. When God therefore bestows life and perpetual duration, it comes to pass that even souls which did not previously exist should henceforth endure, since God has both willed that they should exist, and should continue in existence.
— Irenaeus, Against Heresies, Bk. 2 Ch. 34 4
And so it is written, “The first man Adam became a living being.” The last Adam became a life-giving spirit.
–1 Cor.15:45