Sin is breaking the law of God (I John 3:4). The law of God says such things as do not lie, do not steal, etc. These are moral commands and are intended for people, not animals. Animals don’t have moral beliefs, nor do they have consciences. Also, animals are not made in the image of God as mankind is (Genesis 1:26), and are not under the moral laws intended for people. Therefore, they can’t sin. Animals work off of instinct, not off of moral purpose or obligation to honor God, and not with any spiritual connection to God.
Adam represented all mankind and the animal kingdom. When he sinned, the world was affected by it. Through him sin entered the world (Romans 5:12), which is why we have plagues, famines, etc. Until Adam sinned, there is no record in the Bible about any animal dying. God clothed Adam and Eve with the coat/skin of an animal/animals (Genesis 3:21).