What three reasons does Virgil give for Juno's anger in the Aeneid?
Virgil opens Book 1 of the Aeneid by introducing his hero (though, like Odysseus, unnamed for many lines) and asking for the reasons why Juno, the queen of the gods, drove the man into so many difficulties. The narrative voices gives several reasons, and then another is added in Juno's own words through the poet's characterization of her.
First, there is the issue of Carthage. Juno not only loves this city (lines 15-16), but also wants it to be the future world empire (lines 17-18). Rome, however, would eventually defeat and destroy Carthage—an event which was history for Virgil but is set in the poem as a prophecy or fate that Juno somehow hears of (lines 19-22)—and she is described more as afraid of this outcome than angry (line 23).
Second, she is angry (line 25) at Troy for two reasons: Paris's choice of another goddess in the beauty contest (line 27), and the favor shown to Ganymede, a Trojan youth whom Jupiter loved and lifted to heaven (line 28).
When the poet turns to showing Juno's mood, using characterization rather than exposition (lines 37-49), she is also seen to be angry because her position, power, and influence as a god have been threatened. Athena was allowed to use Jupiter's own lightning to destroy the Greeks she was angry at (lines 39-45). Even though Juno, as queen of the gods and both wife and sister of Jupiter (lines 46-47), should be more important than Athena, she seems to be weak; she has fought the Trojans for many years and yet not defeated them (lines 47-48). The result of this is that no one will bother to worship Juno, since she doesn't seem to have the power to accomplish her goals (lines 48-49).
It depends on which translation you have, but several translations offer at least two of the three reasons:
1) The city of Carthage. As Virgil explains in Book 1, Juno loved the city "beyond all other lands in the world" (ll17-18). Unfortunately, hse knew that men of "Trojan blood" would someday destroy Carthage.
2) She was still angry with Paris (a Trojan) for having not been chosen as the most beautiful of the three goddesses: the Greek versions of their names are probably more familiar to you: Hera, Aphrodite, and Athena.
3) The cup-bearer. Hebe, Juno's daughter, was once cup-bearer to the gods. Some sources (often Greek) claim that she gave up her position to marry Hercules/Herakles. Whatever the reason for her absence from the post, she was replaced by Ganymede, said to be a youth so beautiful that her husband (Jupiter/Zeus) fell in love with him and placed him in Hebe's position. Other versions say that Ganymede was the illegitimate son of Juno's husband; in any case, Juno fiercely resented the young man.
Virgil, The Aeneid. Translated by Robert Fagles. Penguin Books, 2006.