What the Bible says and what you seem to be implying are two different things. I'd prefer to focus on our responsibility for being the stewards for the Earth, now the power trip of trying to "dominate" anything.
Just to add another reply. We humans don't dominate the earth just because we try hard to do it. We dominate the earth simply by existing and living. Some examples would be: cutting down forests, taking over land for homes, farming, building cities, building roads, etc. These acts aren't meant to dominate anything. People are simply living, and just by doing that, they dominate the earth over other animals.
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