Because this is really and truly the body and blood, soul and divinity of Christ, receiving Holy Communion, God's intimate visit with His faithful souls, is most sacred.
When believers receive Holy Communion, they're intimately united with their Lord and Savior, Jesus Christ. However, Communion isn't limited to the communicant (the one receiving Holy Communion) and Jesus Christ. By taking Holy Communion, the Catholic is also expressing her union with all Catholics around the world and at all times who believe the same doctrines, obey the same laws, and follow the same leaders.
This is why Catholics (and Eastern Orthodox Christians) have a strict law that only people who are in communion with the Church can receive Holy Communion. In other words, only those who are united in the same beliefs — the seven sacraments, the authority of the pope, and the teachings in the Catechism of the Catholic Church — are allowed to receive Holy Communion.In the Protestant tradition, Communion is often seen as a means of building unity among various denominations, and many have open Communion, meaning that any baptized Christian can take Communion in their services. Catholics and Eastern Orthodox Christians, on the other hand, see Communion not as the means but as the final fruit of unity. So only those in communion can receive Holy Communion. It has nothing to do with who's worthy.
Think of it this way: If a Canadian citizen moves to the United States, lives in Erie, Pennsylvania, works in Erie, and has a family in Erie, he can do so indefinitely. However, he can't run for public office or vote in an American election unless and until he becomes a U.S. citizen. Does being or not being a citizen make you a good or bad person? Of course not. But if citizens from other countries want to vote, they must give up their own citizenship and become U.S. citizens.
Being a non-Catholic in the Church is like being a non-citizen in a foreign country. Non-Catholics can come to as many Catholic Masses as they want; they can marry Catholics and raise their children in the Catholic faith, but they can't receive Holy Communion in the Catholic Church until they become Catholic. Becoming Catholic is how a person gets united with and experiences union with the whole Catholic Church. Those in union can then receive Holy Communion.
Similarly, Catholics who don't follow the Church's laws on divorce and remarriage, or who obstinately reject Church teaching, such as the inherent evil of abortion, shouldn't come forward to receive Communion because they're no longer in communion. This prohibition isn't a judgment on their moral or spiritual state because only God can know that. But receiving Holy Communion is a public act, and therefore, it's an ecclesiastical action requiring those who do it to be united with all that the Church teaches and commands and with all the ways that the Church prays.