I dug out "The New English Bible" (1970) that I have.<quoted text>
I have showed you in Genesis where God only says that Adam was to eat from the tree of life to live forever.
I have also showed you from Ecclesiastes where Solomon says that God made mankind like the animals so that he does just like they die.
God created man above the animals. It was for man, alone to live forever. Because of sin, man dies just like the animals.
Imagine what the world would be like if nothing ever dies? If every blade of grass, tree, flower kept living forever. Every beetle, grass-hopper and spider lived forever. Every rabbit, mouse and deer lived forever.
The world would be over run in a few years with no room for anything.
Only humans have children based on rational reasoning rather instinct.
So when the scripture says that death will be no more, it is talking about the death that we inherited from Adam. It means ADAMIC death will be no more.
But people can still die. The lake of fire (the second death) remains forever. So people will always be able to experience the second death.
When animals dies they do not die with the hope of a resurrection. Adam's sacrifice does not cover the death of animals. Animals did not inherit sin from Adam.
So animals do not die because they sin, they die because that's how they were designed.
In dealing with men it is God's purpose to test them and to see what they truly are. For man is a creature of chance and the beasts are creatures of chance, and one mischance awaits them all: death comes to both alike. They all draw the same breath. Men have no advantage over beasts; for everything is emptiness. All go to the same place: all come from the dust, and to dust all return. Who knows whether the spirit of man goes upward or whether the spirit of beast goes downward to the earth?
"What happens to man, happens to beasts"