How does Catherine cause Eddie's destruction?

To a large extent, Eddie's feelings for Catherine, or Katie as he always calls her, are directly responsible for his downfall. For one thing, he's overprotective towards her. He puts Catherine on a pedestal; to him, she's a Madonna-like figure—virginal, chaste, and pure. Eddie thinks the big old world outside is no place for such an innocent young lady, and he vows to protect her come what may, determined to live up to the promise he made to Catherine's mother on her deathbed.
Because he's so overprotective, Eddie is strongly opposed to Catherine going on dates. Men will take advantage of her innocence, he thinks; but by keeping her all cooped-up at home where he can keep an eye on her, he's making it harder for Catherine to lead any kind of life out there in the real world. Nevertheless, Eddie can't prevent the world outside from entering the confines of his home, no matter how hard he tries. For when Marco and Rodolpho come to stay, Eddie's whole world starts to collapse, and with it the control he's exercised over Catherine's life.
Eddie senses that he's losing Catherine to Rodolpho. This makes him ever more desperate to win her back. It's too late, however; Catherine's growing into a woman, capable of making her own decisions in life. She's finally able to break free from Eddie's stifling control, which never allowed her to develop properly. Eddie is so set in his ways, so used to getting what he wants, that he can't face the changing reality. He resorts to desperate measures to drive a wedge between Rodolpho and Catherine, calling the immigration department to try and get Rodolpho and Marco deported back to Italy.
Despite her growing maturity, Catherine still feels guilty at Eddie's death, that she's somehow responsible for what happened. It would be more accurate, however, to say that it is Eddie's uncontrollable feelings for Catherine that cause his destruction, rather than Catherine herself.