The husband and wife administer the sacrament of matrimony to one another through their mutual consent to be wed. The priest or deacon acts as a witness and confers a blessing upon the couple, but he does not administer the sacrament of matrimony.
The Church believes that Christ's presence at the wedding at Cana is confirmation of matrimony's goodness. St. Paul compares the relationship between husband and wife to the relationship between Christ and the Church. Christ explicitly forbade divorce in the Gospels, and the Church teaches that a valid sacramental marriage cannot be dissolved by any power on earth except death.