Objection 1. It would seem that the witnesses of the transfiguration were unfittingly chosen. For everyone is a better witness of things that he knows. But at the time of Christ's transfiguration no one but the angels had as yet any knowledge from experience of the glory to come. Therefore the witnesses of the transfiguration should have been angels rather than men.
Objection 2. Further, truth, not fiction, is becoming in a witness of the truth. Now, Moses and Elias were there, not really, but only in appearance; for a gloss on Luke 9:30, "They were Moses and Elias," says: "It must be observed that Moses and Elias were there neither in body nor in soul"; but that those bodies were formed "of some available matter. It is also credible that this was the result of the angelic ministries, through the angels impersonating them." Therefore it seems that they were unsuitable witnesses.
Objection 3. Further, it is said (Acts 10:43) that "all the prophets give testimony" to Christ. Therefore not only Moses and Elias, but also all the prophets, should have been present as witnesses.
Objection 4. Further, Christ's glory is promised as a reward to all the faithful (2 Corinthians 3:18; Philippians 3:21), in whom He wished by His transfiguration to enkindle a desire of that glory. Therefore He should have taken not only Peter, James, and John, but all His disciples, to be witnesses of His transfiguration.
On the contrary is the authority of the Gospel.
I answer that, Christ wished to be transfigured in order to show men His glory, and to arouse men to a desire of it, as stated above (Article 1). Now men are brought to the glory of eternal beatitude by Christ--not only those who lived after Him, but also those who preceded Him; therefore, when He was approaching His Passion, both "the multitude that followed" and that "which went before, cried saying: 'Hosanna,'" as related Matthew 21:9, beseeching Him, as it were, to save them. Consequently it was fitting that witnesses should be present from among those who preceded Him--namely, Moses and Elias--and from those who followed after Him--namely, Peter, James, and John--that "in the mouth of two or three witnesses" this word might stand.
Reply to Objection 1. By His transfiguration Christ manifested to His disciples the glory of His body, which belongs to men only. It was therefore fitting that He should choose men and not angels as witnesses.
Reply to Objection 2. This gloss is said to be taken from a book entitled On the Marvels of Holy Scripture. It is not an authentic work, but is wrongly ascribed to St. Augustine; consequently we need not stand by it. For Jerome says on Matthew 17:3: "Observe that when the Scribes and Pharisees asked for a sign from heaven, He refused to give one; whereas here in order to increase the apostles' faith, He gives a sign from heaven, Elias coming down thence, whither he had ascended, and Moses arising from the nether world." This is not to be understood as though the soul of Moses was reunited to his body, but that his soul appeared through some assumed body, just as the angels do. But Elias appeared in his own body, not that he was brought down from the empyrean heaven, but from some place on high whither he was taken up in the fiery chariot.
Reply to Objection 3. As Chrysostom says on Matthew 17:3: "Moses and Elias are brought forward for many reasons." And, first of all, "because the multitude said He was Elias or Jeremias or one of the prophets, He brings the leaders of the prophets with Him; that hereby at least they might see the difference between the servants and their Lord." Another reason was "... that Moses gave the Law... while Elias... was jealous for the glory of God." Therefore by appearing together with Christ, they show how falsely the Jews "accused Him of transgressing the Law, and of blasphemously appropriating to Himself the glory of God." A third reason was "to show that He has power of death and life, and that He is the judge of the dead and the living; by bringing with Him Moses who had died, and Elias who still lived." A fourth reason was because, as Luke says (9:31), "they spoke" with Him "of His decease that He should accomplish in Jerusalem," i.e. of His Passion and death. Therefore, "in order to strengthen the hearts of His disciples with a view to this," He sets before them those who had exposed themselves to death for God's sake: since Moses braved death in opposing Pharaoh, and Elias in opposing Achab. A fifth reason was that "He wished His disciples to imitate the meekness of Moses and the zeal of Elias." Hilary adds a sixth reason--namely, in order to signify that He had been foretold by the Law, which Moses gave them, and by the prophets, of whom Elias was the principal.
Reply to Objection 4. Lofty mysteries should not be immediately explained to everyone, but should be handed down through superiors to others in their proper turn. Consequently, as Chrysostom says (on Matthew 17:3), "He took these three as being superior to the rest." For "Peter excelled in the love" he bore to Christ and in the power bestowed on him; John in the privilege of Christ's love for him on account of his virginity, and, again, on account of his being privileged to be an Evangelist; James on account of the privilege of martyrdom. Nevertheless He did not wish them to tell others what they had seen before His Resurrection; "lest," as Jerome says on Matthew 17:19, "such a wonderful thing should seem incredible to them; and lest, after hearing of so great glory, they should be scandalized at the Cross" that followed; or, again, "lest [the Cross] should be entirely hindered by the people" [Bede, Hom. xviii; cf. Catena Aurea; and "in order that they might then be witnesses of spiritual things when they should be filled with the Holy Ghost" [Hilary, in Matth. xvii].
Source: Summa Theologica (New Advent)