Thomas Aquinas, Compendium of Theology

The same reasons reveal why Christ willed to suffer the death of the cross. In the first place, such a death was suitable as a salutary means of satisfaction. Man is fittingly punished in the things wherein he has sinned, as is said in Wisdom 11:17: "By what things a man sinneth, by the same also he is tormented." But the first sin of man was the fact that he ate the fruit of the tree of knowledge of good and evil, contrary to God's command. In his stead Christ permitted Himself to be fastened to a tree, so that He might pay for what He did not carry off, as the Psalmist says of Him in Psalm 58:5.

Death on the cross was also appropriate as a sacrament. Christ wished to make clear by His death that we ought so to die in our carnal life that our spirit might be raised to higher things. Hence He Himself says, in John 12:32: "I, if I be lifted up from the earth, will draw all things to Myself."

This kind of death was likewise fitting as an example of perfect virtue. Sometimes men shrink no less from a disgraceful kind of death than from the painfulness of death. Accordingly, the perfection of virtue seems to require that a person should not refuse to suffer even a disgraceful death for the good of virtue. Therefore, to commend the perfect obedience of Christ, the Apostle, after saying of Him that He was "obedient unto death," added: "even to the death of the cross" (Phil. 2:8). This sort of death was looked on as the most ignominious of all, in the words of Wisdom 2:20: "Let us condemn him to a most shameful death."