God has complete sovereign power over His creation and has delegated the authority to mankind to “subdue” the earth – to have dominion over the animals, among others. Mankind was placed in an elevated role position of command and was to exercise dominion over the earth.
God’s command to subdue the earth, it is an authority to have the mastery over all of it.

“And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth”. Genesis 1:26

A genuine mastery cannot be achieved without the comprehension of the thing to be mastered. In order for a pianist  to master the piano, he or she must “practice” and “understand” the instrument. In order for mankind to “subdue” the animal kingdom, he must understand the animals.

‘With great power comes great responsibility ~ “Spider Man” ’. There is a fundamental accountability of being a good steward in the command given by God to mankind to subdue the earth; and with the authority to rule, there is the responsibility to rule justly and it does not suggest cruelty, maltreatment and exploitation – it is to care for, cultivate and employ the animals to their fullest potential in an appropriate and humane manner.

Created in the image of God, Adam and Eve were to use planet earth’s enormous resources and be good and responsible caretakers. This is God’s blessing to mankind.
At the time the command was given to man, man and animals do not eat meat.

And God said, Behold, I have given you every herb bearing seed, which is upon the face of all the earth, and every tree, in the which is the fruit of a tree yielding seed; to you it shall be for meat. Genesis 1:29 (Highlights – mine).

After the Fall of Man and the Floods, men can eat meat. Human continued rule over animals are to be humane – it does not mean they have the right to ill-treat or abuse the animals. (The current gross cruelty, heartlessness and viciousness by humans on the animals are the result of sin that entered into this world).

And God blessed Noah and his sons, and said unto them, Be fruitful, and multiply, and replenish the earth. And the fear of you and the dread of you shall be upon every beast of the earth, and upon every fowl of the air, upon all that moveth upon the earth, and upon all the fishes of the sea; into your hand are they delivered. Every moving thing that liveth shall be meat for you; even as the green herb have I given you all things. Genesis 1:29