In the first reading of the 17th Sunday in Ordinary Time, the young king Solomon has been chosen to be king of Israel, even though he's very young and inexperienced in leadership. God appears to Solomon in a dream and invites him to ask for a gift and He will give it to him.
Solomon could have asked for the gift of administration, or leadership training, or a council of elders to help him rule. Instead, he asks for "an understanding heart to judge your people and to distinguish right from wrong."
The readings for the 16th Sunday in Ordinary Time are simply a celebration of man's frailty and God's willingness to reach out and enrich mankind with His goodness.
The first reading sets the stage when the author tells us: "But though you are master of might, you judge with clemency, and with much lenience you govern us ... and you gave your children good ground for hope that you would permit repentance for their sins."
On the Feast of Sts. Peter and Paul, the Church celebrates two of its greatest leaders. Peter was the leader of the apostles and of the universal Church, and Paul was the leader of the Gentiles.
The Church celebrates these two heroes because Christ celebrated His life in them as they set the tone for evangelizing the unfolding Church. Jesus had spent three years evangelizing Peter, and then after Jesus rose from the dead, He gave Paul a crash course in repentance. This crash course was so profound that it energized Paul's ministry to the Gentiles for the rest of his life.
Science tells us that the higher forms of life assimilate the lower forms of life. Thus, vegetative life assimilates mineral life, and animal life assimilates vegetative life. Bread, as such, is not a living thing; therefore it cannot give life, but only sustain life.
Yet, Jesus tells us that He is the living bread that comes down from heaven. He has life from the Father, and in the Eucharist He gives us the life He has from the Father. Hence, Christ in the Eucharist assimilates us into Himself.