Objection 1. It would seem that slight or contempt is not the sole motive of anger. For Damascene says (De Fide Orth. ii, 16) that we are angry "when we suffer, or think that we are suffering, an injury." But one may suffer an injury without being despised or slighted. Therefore a slight is not the only motive of anger.
Objection 2. Further, desire for honor and grief for a slight belong to the same subject. But dumb animals do not desire honor. Therefore they are not grieved by being slighted. And yet "they are roused to anger, when wounded," as the Philosopher says (Ethic. iii, 8). Therefore a slight is not the sole motive of anger.
Objection 3. Further, the Philosopher (Rhet. ii, 2) gives many other causes of anger, for instance, "being forgotten by others; that others should rejoice in our misfortunes; that they should make known our evils; being hindered from doing as we like." Therefore being slighted is not the only motive for being angry.
On the contrary, The Philosopher says (Rhet. ii, 2) that anger is "a desire, with sorrow, for vengeance, on account of a seeming slight done unbecomingly."
I answer that, All the causes of anger are reduced to slight. For slight is of three kinds, as stated in Rhet. ii, 2, viz. "contempt," "despiteful treatment," i.e. hindering one from doing one's will, and "insolence": and all motives of anger are reduced to these three. Two reasons may be assigned for this. First, because anger seeks another's hurt as being a means of just vengeance: wherefore it seeks vengeance in so far as it seems just. Now just vengeance is taken only for that which is done unjustly; hence that which provokes anger is always something considered in the light of an injustice. Wherefore the Philosopher says (Rhet. ii, 3) that "men are not angry--if they think they have wronged some one and are suffering justly on that account; because there is no anger at what is just." Now injury is done to another in three ways: namely, through ignorance, through passion, and through choice. Then, most of all, a man does an injustice, when he does an injury from choice, on purpose, or from deliberate malice, as stated in Ethic. v, 8. Wherefore we are most of all angry with those who, in our opinion, have hurt us on purpose. For if we think that some one has done us an injury through ignorance or through passion, either we are not angry with them at all, or very much less: since to do anything through ignorance or through passion takes away from the notion of injury, and to a certain extent calls for mercy and forgiveness. Those, on the other hand, who do an injury on purpose, seem to sin from contempt; wherefore we are angry with them most of all. Hence the Philosopher says (Rhet. ii, 3) that "we are either not angry at all, or not very angry with those who have acted through anger, because they do not seem to have acted slightingly."
The second reason is because a slight is opposed to a man's excellence: because "men think little of things that are not worth much ado" (Rhet. ii, 2). Now we seek for some kind of excellence from all our goods. Consequently whatever injury is inflicted on us, in so far as it is derogatory to our excellence, seems to savor of a slight.
Reply to Objection 1. Any other cause, besides contempt, through which a man suffers an injury, takes away from the notion of injury: contempt or slight alone adds to the motive of anger, and consequently is of itself the cause of anger.
Reply to Objection 2. Although a dumb animal does not seek honor as such, yet it naturally seeks a certain superiority, and is angry with anything derogatory thereto.
Reply to Objection 3. Each of those causes amounts to some kind of slight. Thus forgetfulness is a clear sign of slight esteem, for the more we think of a thing the more is it fixed in our memory. Again if a man does not hesitate by his remarks to give pain to another, this seems to show that he thinks little of him: and those too who show signs of hilarity when another is in misfortune, seem to care little about his good or evil. Again he that hinders another from carrying out his will, without deriving thereby any profit to himself, seems not to care much for his friendship. Consequently all those things, in so far as they are signs of contempt, provoke anger.
Source: Summa Theologica (New Advent)