Day 357: God, "Our" Father

When we say "our" Father, we recognize first that all his promises of love announced by the prophets are fulfilled in the new and eternal covenant in his Christ: we have become "his" people and he is henceforth "our" God. This new relationship is the purely gratuitous gift of belonging to each other: we are to respond to "grace and truth" given us in Jesus Christ with love and faithfulness. CCC 2787

In today's reading, the Catechism discusses addressing God as "Our" Father in the Lord's Prayer. We do not do so to "express possession" (as if such were even possible with the Ineffable and Eternal God), but because through Christ we have "an entirely new relationship with God" (CCC 2786). We recognize that the promises of the prophets have been fulfilled in Christ, and "we have become 'his' people and he is henceforth 'our' God" (CCC 2787). We pray "Our" Father because "we personally address the Father of our Lord Jesus Christ," who gave us His Son to redeem us (CCC 2789). 

The Catechism Compendium summarizes why we say "our" Father:

“Our” expresses a totally new relationship with God. When we pray to the Father, we adore and glorify him with the Son and the Holy Spirit. In Christ, we are “his” people, and he is “our” God now and for eternity. In fact, we also say “our” Father because the Church of Christ is the communion of a multitude of brothers and sisters who have but “one heart and mind” (Acts 4:32). (#584)

The Catechism Companion Vol III has some good commentary on this:

We pray as the Church. God is not simply mine; he is ours. Saying "Our Father" signifies our profound connection with him... In praying to God the Father, we acknowledge the Holy Trinity. When we pray the Lord's Prayer, we should be asking God to draw everyone into that love that he poured out on the whole world in sending his Son and giving his Holy Spirit. That is a great thing to long for. The point of prayer is becoming like God and having a humble and trusting heart. (p. 230)