We know from only the fuller context that Eve did not give birth to every single living creature on the earth.
But, (and this is the important part Im pointing out to you) but the Text does clearly say she was the mother of "all the living"
I dont know how the verse reads in your Bible,but I remember my Bible School days, and we had a Bible teacher that taught us from his latin background , and he talked to the cl*** about how the bible actually say something like ""mother of all life"
So from the context we get the idea that this is only talking about her own children, and not in fact, "all the living creatures"
Im just saying that the same Bible says things like all "creation" and all "the world' and its not talking about animals, or trees or birds etc.
Its just talking about people.
so when we might say something like "all of creation follows his teachings"..or "the whole world followed his ideas" we are not talking about the fish and birds and apes and mice or trees etc.
The words like "creation"..."the world",,,the "universe" etc, ...cant be used like automatic blankets to cover everything you can think of every time.
They must be used within their limited given context, and the context for the death that was the result of Adam's sin is given at Romans 5....and it is only talking about human death.
Adam sinned, and death is the result, and it was p***ed down to us via Adam.
Not to our pets.....not to deer...not to cows.....not to worms....just to us who are the children of Adam.
So when Paul tells us that death came to 'all men" it is wrong to twist this into meaning more than what Paul wanted.