Objection 1. It would seem that the sin of the highest angel was not the cause of the others sinning. For the cause precedes the effect. But, as Damascene observes (De Fide Orth. ii), they all sinned at one time. Therefore the sin of one was not the cause of the others' sinning.
Objection 2. Further, an angel's first sin can only be pride, as was shown above (Article 2). But pride seeks excellence. Now it is more contrary to excellence for anyone to be subject to an inferior than to a superior; and so it does not appear that the angels sinned by desiring to be subject to a higher angel rather than to God. Yet the sin of one angel would have been the cause of the others sinning, if he had induced them to be his subjects. Therefore it does not appear that the sin of the highest angel was the cause of the others sinning.
Objection 3. Further, it is a greater sin to wish to be subject to another against God, than to wish to be over another against God; because there is less motive for sinning. If, therefore, the sin of the foremost angel was the cause of the others sinning, in that he induced them to subject themselves to him, then the lower angels would have sinned more deeply than the highest one; which is contrary to a gloss on Psalm 103:26: "This dragon which Thou hast formed--He who was the more excellent than the rest in nature, became the greater in malice." Therefore the sin of the highest angel was not the cause of the others sinning.
On the contrary, It is said (Apocalypse 12:4) that the dragon "drew" with him "the third part of the stars of heaven."
I answer that, The sin of the highest angel was the cause of the others sinning; not as compelling them, but as inducing them by a kind of exhortation. A token thereof appears in this, that all the demons are subjects of that highest one; as is evident from our Lord's words: "Go [Vulg. 'Depart from Me'], you cursed, into everlasting fire, which was prepared for the devil and his angels" (Matthew 25:41). For the order of Divine justice exacts that whosoever consents to another's evil suggestion, shall be subjected to him in his punishment; according to (2 Peter 2:19): "By whom a man is overcome, of the same also he is the slave."
Reply to Objection 1. Although the demons all sinned in the one instant, yet the sin of one could be the cause of the rest sinning. For the angel needs no delay of time for choice, exhortation, or consent, as man, who requires deliberation in order to choose and consent, and vocal speech in order to exhort; both of which are the work of time. And it is evident that even man begins to speak in the very instant when he takes thought; and in the last instant of speech, another who catches his meaning can assent to what is said; as is especially evident with regard to primary concepts, "which everyone accepts directly they are heard" [Boethius, De Hebdom.]. Taking away, then, the time for speech and deliberation which is required in us; in the same instant in which the highest angel expressed his affection by intelligible speech, it was possible for the others to consent thereto.
Reply to Objection 2. Other things being equal, the proud would rather be subject to a superior than to an inferior. Yet he chooses rather to be subject to an inferior than to a superior, if he can procure an advantage under an inferior which he cannot under a superior. Consequently it was not against the demons' pride for them to wish to serve an inferior by yielding to his rule; for they wanted to have him as their prince and leader, so that they might attain their ultimate beatitude of their own natural powers; especially because in the order of nature they were even then subject to the highest angel.
Reply to Objection 3. As was observed above (Question 62, Article 6), an angel has nothing in him to retard his action, and with his whole might he is moved to whatsoever he is moved, be it good or bad. Consequently since the highest angel had greater natural energy than the lower angels, he fell into sin with intenser energy, and therefore he became the greater in malice.
Source: Summa Theologica (New Advent)