Objection 1. It would seem that discord is not a daughter of vainglory. For anger is a vice distinct from vainglory. Now discord is apparently the daughter of anger, according to Proverbs 15:18: "A passionate man stirreth up strifes." Therefore it is not a daughter of vainglory.
Objection 2. Further, Augustine expounding the words of John 7:39, "As yet the Spirit was not given," says (Tract. xxxii) "Malice severs, charity unites." Now discord is merely a separation of wills. Therefore discord arises from malice, i.e. envy, rather than from vainglory.
Objection 3. Further, whatever gives rise to many evils, would seem to be a capital vice. Now such is discord, because Jerome in commenting on Matthew 12:25, "Every kingdom divided against itself shall be made desolate," says: "Just as concord makes small things thrive, so discord brings the greatest things to ruin." Therefore discord should itself be reckoned a capital vice, rather than a daughter of vainglory.
On the contrary stands the authority of Gregory (Moral. xxxi, 45).
I answer that, Discord denotes a certain disunion of wills, in so far, to wit, as one man's will holds fast to one thing, while the other man's will holds fast to something else. Now if a man's will holds fast to its own ground, this is due to the act that he prefers what is his own to that which belongs to others, and if he do this inordinately, it is due to pride and vainglory. Therefore discord, whereby a man holds to his own way of thinking, and departs from that of others, is reckoned to be a daughter of vainglory.
Reply to Objection 1. Strife is not the same as discord, for strife consists in external deeds, wherefore it is becoming that it should arise from anger, which incites the mind to hurt one's neighbor; whereas discord consists in a divergence in the movements of wills, which arises from pride or vainglory, for the reason given above.
Reply to Objection 2. In discord we may consider that which is the term "wherefrom," i.e. another's will from which we recede, and in this respect it arises from envy; and again we may consider that which is the term "whither," i.e. something of our own to which we cling, and in this respect it is caused by vainglory. And since in every moment the term "whither" is more important than the term "wherefrom" (because the end is of more account than the beginning), discord is accounted a daughter of vainglory rather than of envy, though it may arise from both for different reasons, as stated.
Reply to Objection 3. The reason why concord makes small things thrive, while discord brings the greatest to ruin, is because "the more united a force is, the stronger it is, while the more disunited it is the weaker it becomes" (De Causis xvii). Hence it is evident that this is part of the proper effect of discord which is a disunion of wills, and in no way indicates that other vices arise from discord, as though it were a capital vice.
Source: Summa Theologica (New Advent)