In the beginning, that is, during the Dispensation of Innocence (the first dispensation), neither animals nor man had any fear of the other. "And out of the ground the LORD God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them: and whatsoever Adam called every living creature, that was the name thereof. And Adam gave names to all cattle, and to the fowl of the air, and to every beast of the field...." (Gen 2:19-21). Even Satan, appearing as a speaking serpent, did not frighten Adam or Eve (Gen. 3:1-5; Rev. 12:9; 20:2).
Man's peaceful co-existence with animals, with the exception of one "serpent," continued throughout the Dispensation of Conscience (the second dispensation). We know from the food Noah took on the Ark, food for both his family and for the animals, that neither man nor animals were carnivorous (Gen. 6:21). It was not until after the Ark landed that men began to eat, without restriction, animals for food, and animals had the instinct to fear man (Gen. 9:1-6). The carnivorous nature of animals and man will continue until the Dispensation of the Kingdom (the seventh dispensation). At that time, man may still consume meat, but it is doubtful that animals will continue to be carnivorous (Isa. 11:6-9; 65:25).
During the Dispensation of Governments and the Dispensation of Promise (the third and fourth dispensations), there was no change in the diets of animals or man. It was not until the fifth dispensation (the Dispensation of the Law), that God's people were required to change their dietary habits (Lev. 11:3-8; Deut. 14:3-21; etc.). The Dispensation of the Church (the sixth dispensation), once again saw a change in God's dietary instructions. While the Jews are still limited to "kosher foods," the Church has no limitations, whatsoever (Acts 10:10-16; 1 Tim. 4:1-5).
The study of dispensations is the key to understanding the rightly-divided Word of God!