This is from a Google Groups for RCIA members.

Why non-Catholics cannot receive communion:

The best explanation I’ve heard for this came from a conversation between two friends, a Catholic woman and a Protestant woman who happened to be engaged.  The Catholic woman explained it to her friend this way.  It’s like how you and your fiancé are preparing for marriage.  You will be married soon, but haven’t taken your vows yet.  So, for the two of you to engage in the marital act wouldn’t be appropriate yet because that is an act reserved for the marriage covenant.  It is the closest and most intimate experience you will have with another human being.  It’s something not to be enjoyed outside the marriage covenant because it signifies I give myself to you and you give yourself to me.  It’s not until you make a public covenant oath in front of witnesses that you are completely one with one another in all things that you can share that type of communion with one another, that one-flesh bond.

That’s the way it is with the Eucharist.  We believe it’s more than just a symbol.  Scripture calls Christ our bridegroom. As our groom, he has given himself totally and completely to us.  We believe the Eucharist is Christ’s body and blood that He gives to us because we, the Church, are His bride.  When we receive the Eucharist, that’s the closest, most intimate experience we will have with God while here on earth.  In order to enter into this one-flesh covenant communion you need to make a covenant publicly and in front of witnesses saying that it is the Catholic Church and the teachings given to it by Christ that I accept and identify myself with now and forever in order for you to enter into the Catholic experience of Eucharistic communion.

This makes more sense when you consider the that we see the reception of the Eucharist as a sacrament.  The word sacrament comes from the Latin word “sacramentum” which means oath.  But why is making this covenant important?  Because when we say amen to the Eucharist, we aren’t just saying we believe that it is truly Christ’s body and blood.  We are also saying amen to the Church instituted by Christ and the teaching he gave to the Church.

Why is it so important to believe this? 

At Mass, when everyone goes up to receive communion, we don’t approach Christ, our groom, as hundreds of individual brides.  Christ can only have one bride.  Collectively, the Church approaches him as one bride.  How can hundreds of people be one bride?  Because we have a unity of faith.  We have all stood up in front of witnesses and said it’s the Catholic Church and the teaching given to it by Christ that we believe and identify ourselves with.  This communion of faith allows us to collectively approach Christ as his one bride.

Non-Catholics haven’t made this profession of faith so they do not share this unity of faith.  Right now as candidates and catechumenates you can’t make that profession of faith because you are just now learning what those teachings and beliefs are.  Once you learn them, then you will be in a position to make that profession of faith and join the rest of Catholics in a unity of faith and receive Christ in the Eucharist as his bride.  Easter and your first communion is less than three months away!