When Adam sinned, perfect creation was altered by the power of sin (Romans 8: 20). Consequently, the ground grew thorns; pain became part of the fabric of life; and death entered reality. The world became cursed. As such, the animals became affected too. Before sin, they were benign creatures. Afterwards, they violently turned on each other and on humankind.
Is that kind of behavior then considered to be one of sinning? According to the Bible, sinning is the transgression of the Ten Commandments’ Law. Also, outside of the Commandments, sinning is knowing what’s right and refusing to do it (James 4: 17). In humans, that knowledge is written in the heart and mind. Animals don’t have that luxury. They aren’t created as moral, independent beings with the conscious option of knowing the difference between right and wrong. For these reasons, animals are incapable of committing sin.
However, there is a passage in the Bible that may cause a person to come to a different conclusion. It has to do with a covenant God made with Moses. It included a prohibition against the shedding of human blood. In Genesis 9: 5 and 6, God said the following…
“And for your lifeblood I will surely demand an accounting. I will demand an accounting from every animal. And from each human being, too, I will demand an accounting for the life of another human being. Whoever sheds human blood, by humans shall their blood be shed; for in the image of God has God made mankind”
It is not as a punishment for sin that the Lord demanded an accounting of the animal’s actions. It was because when an animal killed a human, it was tantamount to destroying God’s image. This, killing the animal, is a threaded principle throughout the Mosaic law; for example Exodus 21: 28. Incidentally, it is this covenant accounting for the loss of human life that is the basis for capital punishment.
Animals do not and cannot sin. Remember too that it is said that where there is no law, there is no sin (Romans 4: 15; 5: 13). As far as animals are concerned, to them the law is non-existent.