And he said: Let us make man to our image and likeness, and let him have dominion over the fishes of the sea, and the fowls of the air, and the beasts, and the whole earth, and every creeping creature that moves upon the earth. [Genesis1:27]
Some believe that God’s image consists in bearing dominion. This seems not to be the case, because we see many different sorts of animals that exercise dominion: for example, alpha dogs rule the pack; silverback gorillas rule the troop. Consequently there’s nothing uniquely human about bearing dominion.
St Thomas has this to say about the subject:
Not every likeness, not even what is copied from something else, is sufficient to make an image; for if the likeness be only generic, or existing by virtue of some common accident, this does not suffice for one thing to be the image of another. For instance, a worm, though from man it may originate, cannot be called man’s image, merely because of the generic likeness. Nor, if anything is made white like something else, can we say that it is the image of that thing; for whiteness is an accident belonging to many species. But the nature of an image requires likeness in species; thus the image of the king exists in his son: or, at least, in some specific accident, and chiefly in the shape; thus, we speak of a man’s image in copper. Whence Hilary says pointedly that “an image is of the same species.”
Now it is manifest that specific likeness follows the ultimate difference. But some things are like to God first and most commonly because they exist; secondly, because they live; and thirdly because they know or understand; and these last, as Augustine says (QQ. 83, qu. 51) “approach so near to God in likeness, that among all creatures nothing comes nearer to Him.” It is clear, therefore, that intellectual creatures alone, properly speaking, are made to God’s image. [ST Ia q93 a2; emphasis added]
(As an aside, St Augustine held the same, as shown in the quotation)
There is a certain appeal to the notion of image-bearing as dominion-bearing for those of a Reformed bent who hold to what I’ll call an absolutist idea of God’s exercise of His providence, who frequently seem to deny that God works through intermediate causes and (far more importantly) bends the wills of men to do exactly what He wants. On this view of things, it seems pretty clear that the primary (if not the sole) aspect of God’s dealing with creation is the exercise of sovereignty or dominion, so that it’s sensible to conclude that our image-bearing reflects this activity.
But St Thomas says (agreeing with St Augustine):
Man has free-will: otherwise counsels, exhortations, commands, prohibitions, rewards, and punishments would be in vain. [ST Ia q83 a1]
Justice demands that man’s will is free, else God could not justly punish sin nor reward good. Furthermore, Aquinas says elsewhere: “it is in the nature of some things to be contingent. Divine providence does not therefore impose any necessity upon things so as to destroy their contingency” (ST Ia q22 a4). But if God were to exercise His sovereignty so as to compel our wills, it would destroy their contingency. Therefore He does not do so. Rather, the greatness of His Providence is such that without compelling us, His will is done. God’s exercise of authority does not destroy the freedom of creation nor human freedom.
Lastly, it’s probably worth noting that authority on earth is rightly exercised for the common good, not for its own sake. Aquinas says this about law:
from the four preceding articles, the definition of law may be gathered; and it is nothing else than an ordinance of reasonfor the common good, made by him who has care of the community, and promulgated. [ST I-IIa, q90, a4, emphasis added; but read all four articles in the question]
Authority or dominion among men is exercised by means of law, which is an ordinance of reason. Thus it seems that dominion-bearing is subordinate for men to reason, which is consistent with Aquinas’ declaration that the image of God in us consists in the fact that we have rational souls.