Objection 1. It would seem that the motive of anger is not always something done against the one who is angry. Because man, by sinning, can do nothing against God; since it is written (Job 35:6): "If thy iniquities be multiplied, what shalt thou do against Him?" And yet God is spoken of as being angry with man on account of sin, according to Psalm 105:40: "The Lord was exceedingly angry with His people." Therefore it is not always on account of something done against him, that a man is angry.
Objection 2. Further, anger is a desire for vengeance. But one may desire vengeance for things done against others. Therefore we are not always angry on account of something done against us.
Objection 3. Further, as the Philosopher says (Rhet. ii, 2) man is angry especially with those "who despise what he takes a great interest in; thus men who study philosophy are angry with those who despise philosophy," and so forth. But contempt of philosophy does not harm the philosopher. Therefore it is not always a harm done to us that makes us angry.
Objection 4. Further, he that holds his tongue when another insults him, provokes him to greater anger, as Chrysostom observes (Hom. xxii, in Ep. ad Rom.). But by holding his tongue he does the other no harm. Therefore a man is not always provoked to anger by something done against him.
On the contrary, The Philosopher says (Rhet. ii, 4) that "anger is always due to something done to oneself: whereas hatred may arise without anything being done to us, for we hate a man simply because we think him such."
I answer that, As stated above (Question 46, Article 6), anger is the desire to hurt another for the purpose of just vengeance. Now unless some injury has been done, there is no question of vengeance: nor does any injury provoke one to vengeance, but only that which is done to the person who seeks vengeance: for just as everything naturally seeks its own good, so does it naturally repel its own evil. But injury done by anyone does not affect a man unless in some way it be something done against him. Consequently the motive of a man's anger is always something done against him.
Reply to Objection 1. We speak of anger in God, not as of a passion of the soul but as of judgment of justice, inasmuch as He wills to take vengeance on sin. Because the sinner, by sinning, cannot do God any actual harm: but so far as he himself is concerned, he acts against God in two ways. First, in so far as he despises God in His commandments. Secondly, in so far as he harms himself or another; which injury redounds to God, inasmuch as the person injured is an object of God's providence and protection.
Reply to Objection 2. If we are angry with those who harm others, and seek to be avenged on them, it is because those who are injured belong in some way to us: either by some kinship or friendship, or at least because of the nature we have in common.
Reply to Objection 3. When we take a very great interest in a thing, we look upon it as our own good; so that if anyone despise it, it seems as though we ourselves were despised and injured.
Reply to Objection 4. Silence provokes the insulter to anger when he thinks it is due to contempt, as though his anger were slighted: and a slight is an action.
Source: Summa Theologica (New Advent)