The disciples think they're helping Jesus in his Kingdom of God work by shooing the children away. Jesus shocks them by telling them that if they want to be a part of the Kingdom they need to become like those children! In this lesson, we consider Jesus' example to understand what it means to have a child-like faith.
In teaching the truth of God's will regarding divorce, Jesus teaches all disciples an invaluable lesson of discipleship. Disciples seek the will of God, not loopholes for their own will.
John and the other apostles saw themselves positioned as elites in the Kingdom of God Jesus was establishing. However, when their words and actions bring this to Jesus' attention, he rebukes them. He reminds them that they are disciples not the master. As disciples, it is their place to serve Jesus along with others Jesus may call into service. If John or even Peter get in the way of the service others are offering to Jesus, it is John or Peter who is at risk of being "cut off" from the Kingdom, and from eternal life. The warning is to all of us: "be at peace with one another."
Jesus taught the disciples to welcome mere children in Jesus' name. John responds by telling about an exorcist that John and the others prevented from doing such work in Jesus' name. Jesus takes that opportunity to teach all of his disciples how to recognize one another and have fellowship with many new friends in his Kingdom.