Objection 1. It seems that no creature can be like God. For it is written (Psalm 85:8): "There is none among the gods like unto Thee, O Lord." But of all creatures the most excellent are those which are called participation gods. Therefore still less can other creatures be said to be like God.
Objection 2. Further, likeness implies comparison. But there can be no comparison between things in a different "genus." Therefore neither can there be any likeness. Thus we do not say that sweetness is like whiteness. But no creature is in the same "genus" as God: since God is no "genus," as shown above (Question 3, Article 5). Therefore no creature is like God.
Objection 3. Further, we speak of those things as like which agree in form. But nothing can agree with God in form; for, save in God alone, essence and existence differ. Therefore no creature can be like to God.
Objection 4. Further, among like things there is mutual likeness; for like is like to like. If therefore any creature is like God, God will be like some creature, which is against what is said by Isaias: "To whom have you likened God?" (Isaiah 40:18).
On the contrary, It is written: "Let us make man to our image and likeness" (Genesis 1:26), and: "When He shall appear we shall be like to Him" (1 John 3:2).
I answer that, Since likeness is based upon agreement or communication in form, it varies according to the many modes of communication in form. Some things are said to be like, which communicate in the same form according to the same formality, and according to the same mode; and these are said to be not merely like, but equal in their likeness; as two things equally white are said to be alike in whiteness; and this is the most perfect likeness. In another way, we speak of things as alike which communicate in form according to the same formality, though not according to the same measure, but according to more or less, as something less white is said to be like another thing more white; and this is imperfect likeness. In a third way some things are said to be alike which communicate in the same form, but not according to the same formality; as we see in non-univocal agents. For since every agent reproduces itself so far as it is an agent, and everything acts according to the manner of its form, the effect must in some way resemble the form of the agent. If therefore the agent is contained in the same species as its effect, there will be a likeness in form between that which makes and that which is made, according to the same formality of the species; as man reproduces man. If, however, the agent and its effect are not contained in the same species, there will be a likeness, but not according to the formality of the same species; as things generated by the sun's heat may be in some sort spoken of as like the sun, not as though they received the form of the sun in its specific likeness, but in its generic likeness. Therefore if there is an agent not contained in any "genus," its effect will still more distantly reproduce the form of the agent, not, that is, so as to participate in the likeness of the agent's form according to the same specific or generic formality, but only according to some sort of analogy; as existence is common to all. In this way all created things, so far as they are beings, are like God as the first and universal principle of all being.
Reply to Objection 1. As Dionysius says (Div. Nom. ix), when Holy Writ declares that nothing is like God, it does not mean to deny all likeness to Him. For, "the same things can be like and unlike to God: like, according as they imitate Him, as far as He, Who is not perfectly imitable, can be imitated; unlike according as they fall short of their cause," not merely in intensity and remission, as that which is less white falls short of that which is more white; but because they are not in agreement, specifically or generically.
Reply to Objection 2. God is not related to creatures as though belonging to a different "genus," but as transcending every "genus," and as the principle of all "genera."
Reply to Objection 3. Likeness of creatures to God is not affirmed on account of agreement in form according to the formality of the same genus or species, but solely according to analogy, inasmuch as God is essential being, whereas other things are beings by participation.
Reply to Objection 4. Although it may be admitted that creatures are in some sort like God, it must nowise be admitted that God is like creatures; because, as Dionysius says (Div. Nom. ix): "A mutual likeness may be found between things of the same order, but not between a cause and that which is caused." For, we say that a statue is like a man, but not conversely; so also a creature can be spoken of as in some sort like God; but not that God is like a creature.
Source: Summa Theologica (New Advent)