First of all, Jesus instructed that we pray this way, saying “our” (hemon in Greek) Father. So, to be faithful to His command, we pray using the word “our” rather than “my.” Secondly, Jesus wanted us to know that we never pray alone; we always belong to the family of God because we are all children of God.
My brother is not your brother, but my brother and I can say, “She is our mother.” Using that word affirms the relationship of those who use it. The words “we,” “us,” and “ours” designate a communal relationship. Christ is our brother, and God is our Father. Praying the Our Father is meant to reaffirm those basic connections.
Christianity uses the cross as its most ancient symbol. The two bars, horizontal and vertical, also represent the two dimensions of our human existence. There is the transcendent personal relationship between us and God, and there is the immanent relationship between us and our neighbors.