Although the Vatican has never formally taught that cremation is a valid alternative to the “burial of the dead” (as the Church puts it, “the Sacrament of the dead which is administered to the dying from the body of Christ under the sign of the cross”), Catholics who believe in these practices also believe that the Holy See should support their choice as a means of honoring their departed. The Catholic Church is the authority of the Catholic Church–not the Church of Rome–and it is only proper that it should help Catholics to be aware of the difference between the Church, the body of Christ, and the Church of Rome.
When the Church speaks on the Eucharistic aspect of cremation, it says that this is a personal, not a public, act:
The Church and her priests have no power to judge the truth of any form of Eucharistic confession. But all people must recognize that to say one is an atheist does not deprive one of the dignity which the Catholic Church enjoys as the head of the Christian people. (Catechism, no. 815)
In other words, if a Catholic tells you that she or he is a Catholic, that doesn’t mean that she or he is a Catholic. It also doesn’t mean that she or he is a Catholic, but it does mean that she or he believes that this is the way that the Church works with its Eucharistic offerings. This statement confirms the fact that cremation is different from “burial.”
Finally, the above text gives a sense of the Catholic Church’s position regarding the burial of the dead:
The Catholic Church offers special care at the moment of death to souls who have been separated from the body of the Body of Jesus Christ and who are deprived of access to the Eucharist. (Catechism, no. 851)
So, by this text, cremation is in some sense an alternative because the Catholic Church doesn’t officially say “no” if cremation is offered.
In fact, if someone asks you if you’re a Catholic and you deny that being Catholic is a belief, you’re not talking to a Catholic. You’re just telling someone that you’re not a Catholic. Catholic people who give false answers to this question aren’t answering to God, and are really talking to someone (or something else) else. But the truth is that cremation is a way of celebrating the Body of Christ in the most personal way that the Church