Why can't non-Catholics receive Holy Communion in the Catholic Church?

Catholics believe in the Real Presence of Jesus in the Eucharist, meaning that what appears to be bread and wine is really Jesus’ body and blood—not just a symbol of his body and blood. When Catholics receive Holy Communion, it is an expression of the unity among all those in communion with the Catholic Church throughout the world, who maintain the belief in the Real Eucharistic Presence of Christ. Therefore, only those who believe in the True Presence may participate in this sacrament of oneness with Christ and his Church. “… [T]he celebration of the Eucharistic sacrifice is wholly directed toward the intimate union of the faithful with Christ through communion” (CCC 1382). 
 
Ultimately, Catholics believe that we cannot celebrate this unifying sacrament with other Christians while there are disagreements about the Eucharist itself. However, Catholics pray for the day when we can reconcile with other Christians and share in the unity of God’s people through the Holy Eucharist. 
 
The United States Conference of Catholic Bishops expresses this desire for unity: 
 
“We pray that our common baptism and the action of the Holy Spirit in this Eucharist will draw us closer to one another and begin to dispel the sad divisions which separate us. We pray that these will lessen and finally disappear, in keeping with Christ’s prayer for us ‘that they may all be one’” (John 17:21).