The following has been taken from the book “Pastoral Answers” by M. Francis Mannion and published by Our Sunday Visitor.
“The Catholic view of Communion is that in the Eucharist we don’t only receive Christ in a personal way. We are also expressing and deepening our commitment to the living Body of Christ, his Church on earth. To receive Communion in the Catholic Church is affirm publicly all that the Catholic Church belies, teaches and does. When we walk to the altar of the Lord in a Catholic Church, we are expressing belief in the Catholic doctrine of the real presence of Christ, in Catholic teaching about the authoritative role of the papacy and the episcopacy, in the Catholic moral tradition - in short, in the whole of Catholicism.”
This is why it is not proper for the Church to offer the Eucharist to non-Catholics. It is not out of a lack of charity. We as Catholics wish that all could truly participate in the Eucharist, but as this excerpt clearly points out, this evolves more that just cuing up in Communion Line.