Juno hates the Trojans for two reasons the poem gives at the very beginning: an old grudge against Troy, tied to the judgment of Paris, who preferred Venus, and to the abduction of Ganymede; and love for Carthage, the city that destiny promises to destroy at the hands of descendants of the Trojans.
The narrator asks the Muse, "can such anger dwell in the minds of gods?" and receives no direct answer. Juno speaks to herself: "I, defeated, give up what I began?" She knows that destiny is against her, and that is what enrages her. What moves her is the honor of the queen of the gods, offended, for she recalls that Pallas was able to sink a Greek fleet because of one man alone, and the fear that no one will worship her anymore if she yields.
Her hatred changes target over the course of the poem. In Book 1 she bribes Aeolus, who unleashes the storm. In Book 4 she proposes marrying Dido and Aeneas to hold him in Carthage. In Book 7, seeing the Trojans already building in Latium, she admits that Lavinia will indeed be Aeneas's wife and chooses to delay and to drench the land in blood: "if I cannot bend the gods above, I will move Acheron," and she sends the Fury Alecto. In Book 10, she answers Venus that Venus was able to take Aeneas from the hands of the Greeks and turn the fleet into nymphs, and that only Juno accuses herself of having helped the Rutulians.
When Jupiter forbids her to go on, in Book 12, she yields and asks for one thing only: that the Latins keep their name, speech, and dress, and that Troy fall "with its name." The reader weighs whether the reasons suffice. Juno does not have a reason equal to years of persecution, and that is why the poem seems less interested in the cause than in the disproportion of the suffering.