"Man" is the second word of the Aeneid, the first being "arms" or "weapons." Epic poetry was the most characteristically masculine genre in the ancient world, dealing with battles, empire-building, and high adventure, while lyric poets wrote about parties and love affairs.
The Latin word for man, "vir," is the root of both "virile" and "virtue." The latter of these two is a direct translation of "virtus," meaning the quality of strength and devotion to duty appropriate to a good man. Aeneas is notable for this quality, which is second only to his "pietas," his sense of what is due to the gods.
When Aeneas deviates from his course of masculine duty in the first third of the Aeneid, it is because of his love affair with Dido. The decadent luxury of Dido's court is continually associated with femininity, and it is essential for Aeneas's masculine, empire-building mission that he should repudiate this and desert the queen. Dido shows that love means more to her than empire by the manner of her death, while Aeneas asserts the opposite, putting public duty before personal feelings like a good Roman.
Femininity and luxury are both associated with the East in the description of Dido and her court (since Dido, though she is now Queen of Carthage, comes originally from Tyre). This is a problem for Aeneas when he arrives in Italy, since he is regarded as the effete, effeminate foreign invader compared with Turnus, the native Italian. It is therefore necessary for him to defeat Turnus in battle to show his masculine superiority and fitness for rule.