Objection 1. It would seem that envy is not a capital vice. For the capital vices are distinct from their daughters. Now envy is the daughter of vainglory; for the Philosopher says (Rhet. ii, 10) that "those who love honor and glory are more envious." Therefore envy is not a capital vice.
Objection 2. Further, the capital vices seem to be less grave than the other vices which arise from them. For Gregory says (Moral. xxxi, 45): "The leading vices seem to worm their way into the deceived mind under some kind of pretext, but those which follow them provoke the soul to all kinds of outrage, and confuse the mind with their wild outcry." Now envy is seemingly a most grave sin, for Gregory says (Moral. v, 46): "Though in every evil thing that is done, the venom of our old enemy is infused into the heart of man, yet in this wickedness the serpent stirs his whole bowels and discharges the bane of spite fitted to enter deep into the mind." Therefore envy is not a capital sin.
Objection 3. Further, it seems that its daughters are unfittingly assigned by Gregory (Moral. xxxi, 45), who says that from envy arise "hatred, tale-bearing, detraction, joy at our neighbor's misfortunes, and grief for his prosperity." For joy at our neighbor's misfortunes and grief for his prosperity seem to be the same as envy, as appears from what has been said above (Article 3). Therefore these should not be assigned as daughters of envy.
On the contrary stands the authority of Gregory (Moral. xxxi, 45) who states that envy is a capital sin and assigns the aforesaid daughters thereto.
I answer that, Just as sloth is grief for a Divine spiritual good, so envy is grief for our neighbor's good. Now it has been stated above (Question 35, Article 4) that sloth is a capital vice for the reason that it incites man to do certain things, with the purpose either of avoiding sorrow or of satisfying its demands. Wherefore envy is accounted a capital vice for the same reason.
Reply to Objection 1. As Gregory says (Moral. xxxi, 45), "the capital vices are so closely akin to one another that one springs from the other. For the first offspring of pride is vainglory, which by corrupting the mind it occupies begets envy, since while it craves for the power of an empty name, it repines for fear lest another should acquire that power." Consequently the notion of a capital vice does not exclude its originating from another vice, but it demands that it should have some principal reason for being itself the origin of several kinds of sin. However it is perhaps because envy manifestly arises from vainglory, that it is not reckoned a capital sin, either by Isidore (De Summo Bono) or by Cassian (De Instit. Caenob. v, 1).
Reply to Objection 2. It does not follow from the passage quoted that envy is the greatest of sins, but that when the devil tempts us to envy, he is enticing us to that which has its chief place in his heart, for as quoted further on in the same passage, "by the envy of the devil, death came into the world" (Wisdom 2:24).
There is, however, a kind of envy which is accounted among the most grievous sins, viz. envy of another's spiritual good, which envy is a sorrow for the increase of God's grace, and not merely for our neighbor's good. Hence it is accounted a sin against the Holy Ghost, because thereby a man envies, as it were, the Holy Ghost Himself, Who is glorified in His works.
Reply to Objection 3. The number of envy's daughters may be understood for the reason that in the struggle aroused by envy there is something by way of beginning, something by way of middle, and something by way of term. The beginning is that a man strives to lower another's reputation, and this either secretly, and then we have "tale-bearing," or openly, and then we have "detraction." The middle consists in the fact that when a man aims at defaming another, he is either able to do so, and then we have "joy at another's misfortune," or he is unable, and then we have "grief at another's prosperity." The term is hatred itself, because just as good which delights causes love, so does sorrow cause hatred, as stated above (Question 34, Article 6). Grief at another's prosperity is in one way the very same as envy, when, to Wit, a man grieves over another's prosperity, in so far as it gives the latter a good name, but in another way it is a daughter of envy, in so far as the envious man sees his neighbor prosper notwithstanding his efforts to prevent it. On the other hand, "joy at another's misfortune" is not directly the same as envy, but is a result thereof, because grief over our neighbor's good which is envy, gives rise to joy in his evil.
Source: Summa Theologica (New Advent)