Non-Catholics Receiving Communion At Weddings

My fiancee is not Catholic. Why can't she receive Communion at our wedding Mass?

One of the great fruits of holy Communion, according to the Catechism (No.1396), is that the holy Eucharist makes the Church: ''Those who receive the Eucharist are united more closely to Christ. Through it, Christ unites them to all the faithful in one body — the Church. Communion renews, strengthens and deepens this incorporation into the Church, already achieved by baptism." Therefore, the reception of holy Communion truly unites in communion the Catholic faithful who share the same faith, doctrinal teachings, traditions, sacraments and leadership. Non-Catholics receiving Communion would imply a unity that sadly does not exist but for which we should all pray.

With few exceptions, no non-Catholic may receive Catholic Eucharist at all.  Here are the narrow exceptions. At a Catholic Mass Orthodox Christians are officially welcomed to receive, but they probably not as their own church may levy a sentence of excommunication for those who receive Communion with us. Polish National Catholics and the Assyrians of the East are likewise welcome, and we can receive the sacraments from them if we are gravely ill.
  Actually, not all Catholics may receive Communion. Only those who are in a state of grace can receive the Eucharist. To receive Communion in the Catholic Church is a sign of complete acceptance of Catholic teaching. It is also a sign of complete unity among believers. Unfortunately, Catholic and non-Catholic Christians still do not share such unity. At present, the mutual reception of Communion by Catholics and non-Catholics would not be an honest sign. Because of the inability of non-Catholic Christians to receive Communion, Catholics who are marrying a non-Catholic are usually encouraged not to have a Mass as part of their nuptial liturgy.