"For the wages sin pays is death." (Rom. 6:23)
"That is why, just as through one man sin entered into the world and death through sin, and thus death spread to all men because they had all sinned." (Rom. 5:12)
So why do animals die if they don't sin?
To understand the basics of this, we need to first realize that not everything that is called "perfect" is so in an absolute sense. Perfection in the absolute sense can only be attributed to Jehovah. "Nobody is good, except one, God." (Mark 10:18)
The following quote helps to put this into more of a perspective:
"Perfection of any other person or thing (other that Jehovah God), then, is relative, not absolute. (Compare Ps 119:96.) That is, a thing is "perfect" according to, or in relation to, the purpose or end for which it is appointed by its designer or producer, or the use to which it is to be put by its receiver or user. The very meaning of perfection requires that there be someone who decides when "completion" has been reached, what the standards of excellence are, what requirements are to be satisfied, and what details are essential. Ultimately, God the Creator is the final Arbiter of perfection, the Standard-Setter, in accord with his own righteous purposes and interests.—Rom. 12:2;" -Insight, Vol.2 "Perfection"
When Adam and Eve were first created with perfect bodies, they were created with the potential for eternal life. So having a perfect body does not necessarily mean that one would live forever. For them to have lived forever, they would have had to have been allowed to eat from the tree of life. (Gen. 2:9) So even though they had perfect bodies, unless they were allowed to eat from the tree of life, they still would have grown old and died. Appearantly there is not an actual physiological connection between death and sin. Their punishment for their sin was the withholding of eternal life.
Animals (simply being lower life forms) didn't even have the option of eating from the tree of life and so they just naturally age and die. But because the first human pair were made in God's image, they had the opportunity of eating from the tree of life and live forever.
Some have simply equated the having a perfect body to naturally (never aging or dying of sickness) living forever. But looking at this from this perspective of Jehovah's withholding of Adam and Eve's partaking from the tree of life, it makes sense especially considering that animals naturally age and die.
Insight, Vol. 2 "Life"; Particularly Subheadings: "Aging and Death", "Adam lost life for himself and offspring" and "What Man Needs for Life".
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