One thing students need to realize is that being the hero of a literary and being a hero in the usual American sense of the word are not the same thing. Like Gilgamesh, Achilles, and Odysseus, Aeneas is the central figure in an epic poem. This alone pretty much qualifies him for membership in the "epic hero" club. Also, the fact that he has a divine parent, Venus; survives an encounter with inhabitants of the underworld (see Aeneid 6); goes on a quest that will ultimately lead to his becoming a king; and carries divinely made weapons (see Aeneid 8) are other significant "merit badges" for his "epic hero" sash.
People may not like Aeneas because he leaves Dido, but there was no way in Orcus that one of the founders of Rome was going to live happily ever after with a founder of the Carthaginian race.
People may not like Aeneas because he kills Turnus when he's on his knees begging for mercy, but he's not really doing anything different than Achilles did to Hector or than Odysseus did to the Suitors.
People may not like Aeneas because he doesn't seem to have the physical prowess of Achilles, but he certainly slaughters plenty of the enemy in the last three books of the Aeneid, as in this passage from Aeneid 10:
Caeculus, born of the race of Vulcan, and Umbro
who came from the Marsian hills restored order,
the Trojan raged against them: his sword sliced off Anxur’s
left arm, it fell to the ground with the whole disc of his shield
(Anxur had shouted some boast, trusting the power
of words, lifting his spirit high perhaps, promising
himself white-haired old age and long years):
then Tarquitus nearby, proud in his gleaming armour,
whom the nymph Dryope had born to Faunus of the woods,
exposed himself to fiery Aeneas. (A.S. Kline translation)
People may not like Aeneas because he's not cunning like Odysseus/Ulysses, but "cunning" was not a value that the Romans admired in their leaders. Their leaders were supposed to be steady and careful, which Aeneas typically is. Consider especially Aeneid 3 where Aeneas completely avoids the problem of Scylla and Charybdis by taking a different route. Aeneas may not be that adventurous, but he also made it to Italy with a fair number of his companions alive, which is more than we can say for Odysseus.
So, while we may not like Aeneas and we may not want to be like him, that does not mean he is not an "epic hero." He's not a hero like a professional sports figure, Martin Luther King, Jr., or Gandhi, but he is the central figure in Virgil's epic poem, and that makes him an "epic hero." About that, there can be no debate.