None of us, at any age, can fully understand the mystery of Christ which Holy Communion symbolizes. Christ initiated Holy Communion while observing Passover, which was always a family gathering. Christ reinterpreted the Passover Meal of deliverance from slavery in Egypt to His own remembrance. He would deliver from slavery of sin. Our children should be able to participate in our celebration and remembrance, just as children and families celebrate the Passover.
Communion is a family meal.
John Wesley believed the Lord's Supper was an opportunity for the Holy Spirit to convict of sin and lead persons to salvation in Christ. We must allow the Spirit to work in the lives of all people, including our children. God may speak to a child at the altar. Children learn that they are an important part of the family of God by being able to participate fully in the community of faith. Communion is an important part of this fellowship and to exclude children is to communicate that they are not really a part of the family of God.