I wrote in a previous article titled DO ANIMALS HAVE SOULS? that
the soul of man is different from that of animals in one very important aspect. When God created man He ‘breathed into his nostrils the breath of life and he became a living creature’ (Genesis 1:7). This step gave the soul of man an eternal dimension. This means that after death the soul of man continues to live on forever. This is not the case with the other animals God created. He did not breath into them “the breath of life” as he had done to man. So, the soul of the animal, because it does not have the eternal dimension, dies with the animal and ceases to exist, in my way of understanding.
In Genesis 6:17 the animals that God is about to destroy with the flood have “the breath of life” in them. “For behold, I will bring a flood of waters upon the earth to destroy all flesh in which is the breath of life under heaven. Everything that is on the earth shall die.” The question is, does this verse imply that the life in animals has the same eternal characteristic as it does in humankind?
Let’s see what happened with the man at his creation and compare that with what happened with the animals.
In Genesis 1:6-7,
- The Lord formed the human body of Adam from “the dust of the ground.”
- He then “breathed into his nostrils the breath of life.”
- “The man became a living creature.”
The animals must have undergone a similar process—bodies formed first, and then life was given to their bodies. The bestowing of life to a physical body formed from the dust of the ground makes one “a living creature.” Both man and animals possess life from God. God is the source of all life. It is in this sense that the “breath of life” is in all living creatures (Gen 6:17).
The animals and man are not inanimate like rocks but “living creatures.” God distinguished the animals and man from rocks by imparting life to them. The animals, like people, are “living creatures” having received life from God at the time of their original creation. The animals are equipped to pass on life to their progeny so that their offspring might live as well. In this sense, there is a continuance of life from one generation to the next.
The image of God in man is what differentiates him from the animals. Animals do not have this same characteristic, even though they are “living creatures.” This likeness to God in man means, among other things, an enduring life that does not end with physical death, as it does with the animals. It may be that the act whereby God directly breathed His life into the nostrils of Adam, imprinted this image of God upon the unique soul of man, giving the soul of man a spiritual aspect not apparent in the other animals God created.
More importantly, there is the issue of the quality of Life after physical death, seeing that the soul of man continues to live on after the body has died. Quality of life is not the same for every person in the hereafter. Although the soul of man continues to live on (exist) after death, life on the other side will not be the same for every person. Some will reside in eternal life (as to a quality of existence), and some will live in eternal death (as to a quality of existence).
For the animals, this poses no problem for their souls cease to exist at the time of their death, in my way of understanding. This is not the case with people. God asks each person to trust in Jesus, as the One who came from the Father to die a death for all humankind and be raised into a new kind of life, shared with those who put their faith in Him (Jn 1:10-12; 3:16-19; 10:25-29).
Jesus revealed to Martha, “I am the resurrection and the life. Whoever believes in me, though he die, yet shall he live, and everyone who lives and believes in me shall never die. Do you believe this?” (Jn 11:25-26
Also of importance is the quality and depth of our spiritual lives in the here-and-now. The moment we come to faith in Christ “new life” is breathed into our souls allowing purpose and meaning to our existence and fresh perspective on the mundane (Jn 4:7-21). We are given new capabilities to love God and to love one another.
 The Holy Bible: English Standard Version (Wheaton, IL: Crossway Bibles, 2016), Ge 6:17.