How to accomplish the objective of Christian faith? The GDC give a largely Gospel-flavored presentation:
84. The object of catechesis is realized by diverse, interrelated tasks.* To carry them out, catechesis is certainly inspired by the manner in which Jesus formed his disciples. He made known to them the different dimensions of the Kingdom of God: “to you it has been given to know the secrets of the Kingdom of heaven” (Mt 13,11). (Cf. Mk 4:10-12) He taught them to pray (“When you pray, say Father… Lk 11,2). (Cf. Mt 6: 5-6) He impressed upon them evangelic attitudes (“learn from me for I am gentle and lowly in heart” Mt 11,29) He prepared them for mission (“He sent them on ahead of him two by two…” Lk 10,1) (Cf. Mt 10:5-15)
*The General Catechetical Directory (1971) 21-29 also distinguishes between the end (finis) and the means (munera) of catechesis. These are the specific objectives in which the end is concretized.
From here, the GDC presents why Christian faith is not a private matter. Faith is a communal matter, shared with the people you know and the people you don’t. Especially the latter category:
The duties of catechesis correspond to education of the different dimensions of faith, for catechesis is integral Christian formation, “open to all the other factors of Christian life”. (Catechesi Tradendae 21b) In virtue of its own internal dynamic, the faith demands to be known, celebrated, lived and translated into prayer. Catechesis must cultivate each of these dimensions. The faith, however, is lived out by the Christian community and proclaimed in mission: it is a shared and proclaimed faith. These dimensions must also be encouraged by catechesis. The Second Vatican Council expresses these duties as follows: “…catechetical instruction, which illumines and strengthens the faith develops a life in harmony with the Spirit of Christ, stimulates a conscious and fervent participation in the liturgical mystery and encourages men to take an active part in the apostolate”. (Gravissimum Educationis 4; cf. RCIA 19, canon law 788,2)