John 6:53-56. So Jesus said to them, Truly, truly, I say to you, unless you eat the flesh of the Son of man and drink his blood, you have no life in you; he who eats my flesh and drinks my blood has eternal life, and I will raise him up at the last day. For my flesh is food indeed, and my blood is drink indeed. He who eats my flesh and drinks my blood abides in me, and I in him.
This is the beginning of understanding Holy Communion which was instituted at the Last Supper (Matt 26:26, Mk 15:22-24, Luke 22:19-20). Communion is the celebration of the Eucharist when we consume the body and blood of Christ. It looks like bread and wine, however during mass it is transformed into the body and blood of Christ. This is the central celebration of the Catholic Church.
Jesus clearly seems to indicate te importance of this consumption for our salvation, so why wouldnt the Church want everyone to consume it? This would seem to meet Jesus criteria above, correct? Well, there is some responsibility required when consuming the body and blood of Christ. I'll let Paul explain:
1 Cor 11:27-30. Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of profaning the body and blood of the Lord. Let a man examine himself, and so eat of the bread and drink of the cup. For any one who eats and drinks without discerning the body eats and drinks judgment upon himself. That is why many of you are weak and ill and some have died.
Because the Eucharist is not a symbol, but really the body and blood of Christ, it has power. This entails responsibility for us. The Eucharist is tied into the sacrament of Confession in a very real and powerful way. Confession prepares us for Holy Communion in a perfect way by allowing us to examine ourselves and [discern] the body. This begins to get to the heart of why non-Catholics cannot participate.
The Church limits participation out of concern for souls. In her wisdom, the Church prevent you from eat[ing] and drink[ing] judgment upon yourself. Because non-Catholics do not understand the power of the Eucharist and the sanctity with which we should approach the altar, they are not prepared to accept the responsibility that the Eucharist entails. In other words, if you do not understand what you eat, you cant possibly understand the ramifications of eating it. The Church is protecting you from the inevitable judgment that is so severe that some have died. Thats the power and holiness of God.
1 Cor 10:15-17. I speak as to sensible men: judge for yourselves what I have to say. The cup of blessing which we bless, is it not a participation in the blood of Christ? The bread which we break, is it not a participation in the body of Christ? Because there is one bread, we who are many are one body, for we all partake of the one bread.
It is not a restriction to be petty or mean, but rather a true concern for your soul. Yet the Eucharist continually calls you home to the Catholic Church, so that you may participate in the body and blood of Christ.