God dwells in us. We aren't God.
John 14:16-17 And I will ask the Father, and he will give you another Helper, to be with you forever, even the Spirit of truth, whom the world cannot receive, because it neither sees him nor knows him. You know him, for he dwells with you and will be in you.
Ephesians 3:14-19 For this reason I bow my knees before the Father, from whom every family in heaven and on earth is named, that according to the riches of his glory he may grant you to be strengthened with power through his Spirit in your inner being, so that Christ may dwell in your hearts through faith—that you, being rooted and grounded in love, may have strength to comprehend with all the saints what is the breadth and length and height and depth, and to know the love of Christ that surpasses knowledge, that you may be filled with all the fullness of God.
1 Corinthians 6:18-20 Or do you not know that your body is a temple of the Holy Spirit within you, whom you have from God? You are not your own, for you were bought with a price. So glorify God in your body.
But the CCC does teach that men will become God, so it's no surprise to me that Catholics espouse the same heresy.
http://www.vatican.va/archive/ccc_css/archive/catechism/p122a3p1.htm
460 The Word became flesh to make us "partakers of the divine nature":78 "For this is why the Word became man, and the Son of God became the Son of man: so that man, by entering into communion with the Word and thus receiving divine sonship, might become a son of God."79 "For the Son of God became man so that we might become God."80 "The only-begotten Son of God, wanting to make us sharers in his divinity, assumed our nature, so that he, made man, might make men gods."81
CCC 795, “Christ and his Church thus together make up the “whole Christ”... Let us rejoice then and give thanks that we have become not only Christians, but Christ himself. Do you understand and grasp, brethren, God’s grace toward us? Marvel and rejoice: we have become Christ.”
795 Christ and his Church thus together make up the "whole Christ" (Christus totus). The Church is one with Christ. The saints are acutely aware of this unity:
Let us rejoice then and give thanks that we have become not only Christians, but Christ himself. Do you understand and grasp, brethren, God's grace toward us? Marvel and rejoice: we have become Christ. For if he is the head, we are the members; he and we together are the whole man. . . . The fullness of Christ then is the head and the members. But what does "head and members" mean? Christ and the Church.
Our redeemer has shown himself to be one person with the holy Church whom he has taken to himself.
Head and members form as it were one and the same mystical person.
A reply of St. Joan of Arc to her judges sums up the faith of the holy doctors and the good sense of the believer: "About Jesus Christ and the Church, I simply know they're just one thing, and we shouldn't complicate the matter."