It is an infallible teaching of the Catholic Church that the Eucharist is a sacrifice—in particular, the one sacrifice of Christ. The Council of Trent declared:
If any one saith, that, by the sacrifice of the mass, a blasphemy is cast upon the most holy sacrifice of Christ consummated on the cross; or, that it is thereby derogated from; let him be anathema (The Canons on the Sacrifice of the Mass, canon 4).
The Catechism of the Catholic Church reaffirms Trent’s teaching: “The Eucharist is . . . a sacrifice” (CCC 1365).
The Catholic understanding of the Eucharist rests on the belief that the Last Supper was a sacrifice. Blessed Pope Paul VI, in his 1965 encyclical Mysterium Fidei, called the Last...