Eddie wants justice for himself; he takes his troubles to the law of the land to try and help him find a way to get Rodolfo because he doesn't want him to marry Catherine but once he gets to Alfieri he discovers that there is nothing the law can do to help him. His only option is to tell the authorities about Rodolfo being an illegal immigrant. Because there's nothing illegal about a girl falling in love with an immigrant.
Justice would allow Eddie to sort out his problem with Rodolfo and Catherine, but justice is just a theory, it is what people believe but it isn't he law. The law can take peoples justice away; in this case the law couldn't help Eddie and justice remained.
When Eddie finds that the law can help him, he turns to justice and pride. Eddie tries to embarrass Rodolfo, he feels that if he embarrasses Rodolfo then he is proving a point to Catherine, that she will see that Rodolfo isn't a man.
Eddie challenges Rodolfo to punch him, like a boxer. Rodolfo hits him mildly, but this gives Eddie a reason to hit back. Eddie hit Rodolfo to show his superiority over him, that he was better and deserved Catherine for himself. "I didn't hurt him. Did I hurt you kid?"
Eddie tries to make it seem as if he was only playing and that he didn't really mean to hurt him. This is obvious to us as a reader that...