Don't get us wrong. It's not like Eddie sits in his bedroom plotting evil ways to desert his wife and whisk his niece away to his secret lair. Eddie has thoroughly convinced himself that he is only trying to protect her. He thinks he's acting like any kindly father-figure should. He's protecting her from the despicable young suitor, who just wants to manipulate and desecrate his precious princess. It's interesting that Eddie's obliviousness is probably what allows us to still sympathize with him on some level.
Though his incestuous feelings are thoroughly repressed, it's still screamingly clear that they're there. Case in point: Eddie has stopped having sex with his wife. When pressed to explain why, he says he's worried about Catherine. Not convinced? Think about how nuts Eddie goes whenever anybody suggests the idea. When Alfieri tries to point it out to Eddie, the longshoreman just gets madder and madder. When Beatrice shouts at him, "You want somethin' else, Eddie, and you can never have her!" (2.316), Eddie becomes furious and rushes down the stairs to his death. If these moments don't make it clear, then how about when Eddie forces a kiss on his niece? Of course, at the end of the play, Eddie dies in his wife's arms, moaning "My, B.!" (2.333) Could this mean that, in his last moments, Eddie realizes that Beatrice was the real love his life?