Two views of why specifically Moses and Elijah were chosen to meet Jesus on the mountain:
Why specifically Moses and Elijah appeared is hard to say. Moses had died, but was his body already in heaven, because no one has found his grave? Is that implied by God’s burying him (Deuteronomy 34:6)? Elijah ascended into heaven and so, we may assume, is now coming down from heaven. Yet both men’s appearance is more likely due to how Moses was God’s great envoy at the start of Israel’s national history, as Elijah was in the time of the kings. Both were in their day the maintainers of God’s justice: Moses in giving the law, Elijah in striving for its observance. Both spoke with God on Horeb, where the law was given. Moses and Elijah represent the Law and the Prophets: Moses as mediator of the old dispensation, Elijah as prophet par excellence. Scripture testifies to both men’s uniqueness (Deuteronomy 34:10; Malachi 4:5).
Moses and Elijah are both mentioned at the very end of the Old Testament (Malachi 4:4–5) and both had an unusual departure from the earth (Deuteronomy 34:5–7, 2 Kings 2:11). Moses is called the example (Deuteronomy 18:15), and Elijah the forerunner (Malachi 4:5), of the Messiah . They will also play a joint role in the last days as heavenly witnesses (see Revelation 11:1–14, especially Revelation 11:6).
Interpretation 1:
Why Moses and Elijah specifically appeared is not so easy to say. Moses had died, but was his body nevertheless already in heaven now, because no one has found his grave? Could that be inferred from the fact that God buried him (Deuteronomy 34:6)? Elijah ascended into heaven and as such, we may assume, is now coming down from heaven. Yet their appearance could be better clarified in light of the fact that Moses was the great envoy of God in the first period of Israel’s national existence, as Elijah was during the days of the kings. Both were in their time the great maintainers of the right of God—Moses by giving the law, Elijah by striving for its observance. Both spoke with God on Horeb, the mountain where the law was given. Moses and Elijah call to mind the Law and the Prophets. Moses, after all, is the mediator of the old dispensation, Elijah the prophet par excellence. Of both men a very special testimony is given in Scripture (Deuteronomy 34:10; Malachi 4:5). Both were unique.1
Interpretation 2:
Moses and Elijah are mentioned together in the very last book of the Old Testament, Malachi (see Malachi 4:4–5). Moreover, both had an unusual departure from this world (Deuteronomy 34:5–7, 2 Kings 2:11), and Moses is specifically called the example (Deuteronomy 18:15), and Elijah the forerunner, of the Messiah (Malachi 4:5). They will also play a joint role in the last days as heavenly witnesses (see Revelation 11:1–14, especially Revelation 11:6).2
3 Et voici, Moïse et Elie leur apparurent, s'entretenant avec lui.