Objection 1. It would seem that it is unlawful to curse an irrational creature. Cursing would seem to be lawful chiefly in its relation to punishment. Now irrational creatures are not competent subjects either of guilt or of punishment. Therefore it is unlawful to curse them.
Objection 2. Further, in an irrational creature there is nothing but the nature which God made. But it is unlawful to curse this even in the devil, as stated above (Article 1). Therefore it is nowise lawful to curse an irrational creature.
Objection 3. Further, irrational creatures are either stable, as bodies, or transient, as the seasons. Now, according to Gregory (Moral. iv, 2), "it is useless to curse what does not exist, and wicked to curse what exists." Therefore it is nowise lawful to curse an irrational creature.
On the contrary, our Lord cursed the fig tree, as related in Matthew 21:19; and Job cursed his day, according to Job 3:1.
I answer that, Benediction and malediction, properly speaking, regard things to which good or evil may happen, viz. rational creatures: while good and evil are said to happen to irrational creatures in relation to the rational creature for whose sake they are. Now they are related to the rational creature in several ways. First by way of ministration, in so far as irrational creatures minister to the needs of man. On this sense the Lord said to man (Genesis 3:17): "Cursed is the earth in thy work," so that its barrenness would be a punishment to man. Thus also David cursed the mountains of Gelboe, according to Gregory's expounding (Moral. iv, 3). Again the irrational creature is related to the rational creature by way of signification: and thus our Lord cursed the fig tree in signification of Judea. Thirdly, the irrational creature is related to rational creatures as something containing them, namely by way of time or place: and thus Job cursed the day of his birth, on account of the original sin which he contracted in birth, and on account of the consequent penalties. On this sense also we may understand David to have cursed the mountains of Gelboe, as we read in 2 Samuel 1:21, namely on account of the people slaughtered there.
But to curse irrational beings, considered as creatures of God, is a sin of blasphemy; while to curse them considered in themselves is idle and vain and consequently unlawful.
From this the Replies to the objections may easily be gathered.
Source: Summa Theologica (New Advent)