Through baptism we entered a profound communion with God as sons and daughters. Thus the baptized are brothers and sisters. This communion is in Christ.

By entering a covenant community we are seeking to live fully our baptismal union in Christ and through Him to become one family in committed relationships with brothers and sisters. Far from being an exclusive relationship, it strengthens us to extend our love to all.

Benedict XVI on the meaning of covenant:
To "ratify a Covenant" means "to enter with others into a bond based on blood or to welcome the other into one’s own covenant fellowship and thus to enter into a communion of mutual rights and obligations". In this way, a real, if non-material form of consanguinity is established. The partners become in some way "brothers of the same flesh and the same bones". The covenant brings about a fellowship that means peace (cf. ThWNT II, 105-137). Can we now form at least an idea of what happened at the hour of the Last Supper, and what has been renewed ever since, whenever we celebrate the Eucharist? God, the living God, establishes a communion of peace with us, or to put it more strongly, he creates "consanguinity" between himself and us. Through the incarnation of Jesus, through the outpouring of his blood, we have been drawn into an utterly real consanguinity with Jesus and thus with God himself. The blood of Jesus is his love, in which divine life and human life have become one. Let us pray to the Lord, that we may come to understand ever more deeply the greatness of this mystery. Let us pray that in our innermost selves its transforming power will increase, so that we truly acquire consanguinity with Jesus, so that we are filled with his peace and grow in communion with one another. >>>