I think you are referring to Ecclesiastes 3:18-20, where Solomon wrote......
"I also said in my heart about the sons of men that the true God will test them and show them that they are like animals, 19 for there is an outcome for humans and an outcome for animals; they all have the same outcome. As the one dies, so the other dies; and they all have but one spirit. So man has no superiority over animals, for everything is futile. 20 All are going to the same place. They all come from the dust, and they all are returning to the dust."
When the first humans were formed, Genesis indicates that the Creator educated Adam for some time before producing a mate for him. His expression when God brought her to him, is an indication that Adam had observed all the other creatures with mates, yet there was not one of his kind with whom he could reproduce and fill the earth, like the others.
Humans were created different to all other creatures. Only he reflected the moral qualities of his Creator.
Death is not mentioned in Eden, except as a punishment for disobedience. Hence, no disobedience would have meant no death. The "tree of life" was freely available to humans with no prohibition. They could partake and keep on living indefinitely.
Only when sin entered their lives, did the tree of life become 'off-limits'. God made sure that access to this source of life would never be within their reach whilst sin ruled their lives. They then became just like the animals, dying exactly the same death as they did. It was never meant to be, but abuse of free will had to be dealt with and the outcome fully documented.
This is not what the Bible says. God created all animals kinds and gave them reproductive powers. Whatever God created, he did directly and with purpose. The creative days were not 24 hour time periods. We know that dinosaurs did not share the planet with humans and we are glad that this is so. Its hard enough getting hit by a truck, let alone something 10 times bigger. God had his reasons for those creatures that existed before man, but he does not tell us. All we know is that the creatures that were alive when Adam was created were named by him and he was assigned to take care of them, along with their habitat. Already extinct creatures could not be named if they no longer existed.
Genesis says that humankind were created at the conclusion of the 6th day, when God declared his satisfaction with his creative efforts thus far. The rebellion took place at the beginning of the 7th day....a period set aside for settling any issues relating to the use of free will. It had to be tested. There is no declaration concerning the conclusion of the 7th day, because it has not yet ended. There has to be a conclusion of this system of things, justice meted out to all rebels, and the rulership of God's Kingdom for a thousand years to get everything back to square one, so that God can declare the 7th day a resounding success. What we lost in Genesis is given back to us in Revelation.