Objection 1. It would seem unlawful to curse anyone. For it is unlawful to disregard the command of the Apostle in whom Christ spoke, according to 2 Corinthians 13:3. Now he commanded (Romans 12:14), "Bless and curse not." Therefore it is not lawful to curse anyone.
Objection 2. Further, all are bound to bless God, according to Daniel 3:82, "O ye sons of men, bless the Lord." Now the same mouth cannot both bless God and curse man, as proved in the third chapter of James. Therefore no man may lawfully curse another man.
Objection 3. Further, he that curses another would seem to wish him some evil either of fault or of punishment, since a curse appears to be a kind of imprecation. But it is not lawful to wish ill to anyone, indeed we are bound to pray that all may be delivered from evil. Therefore it is unlawful for any man to curse.
Objection 4. Further, the devil exceeds all in malice on account of his obstinacy. But it is not lawful to curse the devil, as neither is it lawful to curse oneself; for it is written (Sirach 21:30): "While the ungodly curseth the devil, he curseth his own soul." Much less therefore is it lawful to curse a man.
Objection 5. Further, a gloss on Numbers 23:8, "How shall I curse whom God hath not cursed?" says: "There cannot be a just cause for cursing a sinner if one be ignorant of his sentiments." Now one man cannot know another man's sentiments, nor whether he is cursed by God. Therefore no man may lawfully curse another.
On the contrary, It is written (Deuteronomy 27:26): "Cursed be he that abideth not in the words of this law." Moreover Eliseus cursed the little boys who mocked him (2 Kings 2:24).
I answer that, To curse [maledicere] is the same as to speak ill [malum dicere]. Now "speaking" has a threefold relation to the thing spoken. First, by way of assertion, as when a thing is expressed in the indicative mood: in this way "maledicere" signifies simply to tell someone of another's evil, and this pertains to backbiting, wherefore tellers of evil [maledici] are sometimes called backbiters. Secondly, speaking is related to the thing spoken, by way of cause, and this belongs to God first and foremost, since He made all things by His word, according to Psalm 32:9, "He spoke and they were made"; while secondarily it belongs to man, who, by his word, commands others and thus moves them to do something: it is for this purpose that we employ verbs in the imperative mood. Thirdly, "speaking" is related to the thing spoken by expressing the sentiments of one who desires that which is expressed in words; and for this purpose we employ the verb in the optative mood.
Accordingly we may omit the first kind of evil speaking which is by way of simple assertion of evil, and consider the other two kinds. And here we must observe that to do something and to will it are consequent on one another in the matter of goodness and wickedness, as shown above (I-II, 20, 3). Hence in these two ways of evil speaking, by way of command and by way of desire, there is the same aspect of lawfulness and unlawfulness, for if a man commands or desires another's evil, as evil, being intent on the evil itself, then evil speaking will be unlawful in both ways, and this is what is meant by cursing. On the other hand if a man commands or desires another's evil under the aspect of good, it is lawful; and it may be called cursing, not strictly speaking, but accidentally, because the chief intention of the speaker is directed not to evil but to good.
Now evil may be spoken, by commanding or desiring it, under the aspect of a twofold good. Sometimes under the aspect of just, and thus a judge lawfully curses a man whom he condemns to a just penalty: thus too the Church curses by pronouncing anathema. On the same way the prophets in the Scriptures sometimes call down evils on sinners, as though conforming their will to Divine justice, although such like imprecation may be taken by way of foretelling. Sometimes evil is spoken under the aspect of useful, as when one wishes a sinner to suffer sickness or hindrance of some kind, either that he may himself reform, or at least that he may cease from harming others.
Reply to Objection 1. The Apostle forbids cursing strictly so called with an evil intent: and the same answer applies to the Second Objection.
Reply to Objection 3. To wish another man evil under the aspect of good, is not opposed to the sentiment whereby one wishes him good simply, in fact rather is it in conformity therewith.
Reply to Objection 4. In the devil both nature and guilt must be considered. His nature indeed is good and is from God nor is it lawful to curse it. On the other hand his guilt is deserving of being cursed, according to Job 3:8, "Let them curse it who curse the day." Yet when a sinner curses the devil on account of his guilt, for the same reason he judges himself worthy of being cursed; and in this sense he is said to curse his own soul.
Reply to Objection 5. Although the sinner's sentiments cannot be perceived in themselves, they can be perceived through some manifest sin, which has to be punished. Likewise although it is not possible to know whom God curses in respect of final reprobation, it is possible to know who is accursed of God in respect of being guilty of present sin.
Source: Summa Theologica (New Advent)