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Yes, the bible does say, "Ye shall be gods." But that work is not completed. And by "partake," is meant, "to participate, to be given a portion." But we will not be gods in the Mormon or pagan sense. There will be no planets to rule, or forces of nature to control. Those who are saved will be gods in the sense that they shall never die, they shall be indefatiguible and perfected (as opposed to He who is perfect from the beginning).

The notion of deification is unsettling to the modern ear, because it suggests a separate will which can oppose God. That is why context is everything; the passage you cite in the Catechism teaches that godliness is attained through sacrificing one's own self, not glorifying it:

456 With the Nicene Creed, we answer by confessing: "For us men and for our salvation he came down from heaven; by the power of the Holy Spirit, he became incarnate of the Virgin Mary, and was made man."

457 The Word became flesh for us in order to save us by reconciling us with God, who "loved us and sent his Son to be the expiation for our sins": "the Father has sent his Son as the Saviour of the world", and "he was revealed to take away sins":70

Sick, our nature demanded to be healed; fallen, to be raised up; dead, to rise again. We had lost the possession of the good; it was necessary for it to be given back to us. Closed in the darkness, it was necessary to bring us the light; captives, we awaited a Saviour; prisoners, help; slaves, a liberator. Are these things minor or insignificant? Did they not move God to descend to human nature and visit it, since humanity was in so miserable and unhappy a state?71

458 The Word became flesh so that thus we might know God's love: "In this the love of God was made manifest among us, that God sent his only Son into the world, so that we might live through him."72 "For God so loved the world that he gave his only Son, that whoever believes in him should not perish but have eternal life."73

459 The Word became flesh to be our model of holiness: "Take my yoke upon you, and learn from me." "I am the way, and the truth, and the life; no one comes to the Father, but by me."74 On the mountain of the Transfiguration, the Father commands: "Listen to him!"75 Jesus is the model for the Beatitudes and the norm of the new law: "Love one another as I have loved you."76 This love implies an effective offering of oneself, after his example.77

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

Oh, and do check ou the references:

70 I ⇒ Jn 4:10; ⇒ 4:14; ⇒ 3:5.

71 St. Gregory of Nyssa, Orat. catech 15: PG 45, 48B.

72 ⇒ I Jn 4:9.

73 ⇒ Jn 3:16.

74 ⇒ Mt 11:29; ⇒ Jn 14:6.

75 ⇒ Mk 9:7; cf. Dt 6:4-5.

76 ⇒ Jn 15:12.

77 Cf. ⇒ Mk 8:34.

78 ⇒ 2 Pt 1:4.

79 St. Irenaeus, Adv. haeres. 3, 19, 1: PG 7/1, 939.

80 St. Athanasius, De inc. 54, 3: PG 25, 192B.

81 St. Thomas Aquinas, Opusc. 57, 1-4.

82 ⇒ Jn 1:14.

A brief explanation of the Catholic position: http://www.bringyou.to/apologetics/a124.htm