I think this is a good time to start trying to understand the paradox of the cross: It is beyond human understanding, yet contains a divine purpose and profound supernatural love. Through Jesus' death on the cross, he has saved us from a similarly horrible death.
The Crucifixion is a horror method of execution. It was specifically designed to intensify and prolong agony, but to be the ultimate insult to personal dignity, the last word in humiliating and dehumanizing treatment."
And yet, for love of us, Jesus chose to suffer this unimaginably painful, degrading death, because "no other mode of execution would have been commensurate with the extremity of humanity's condition under Sin."
To understand why Christ's passion and death on the cross were necessary for our salvation, we have to understand the idea of sacrifice and atonement in the Old Testament. According to the old Mosaic covenant, priests would offer animal sacrifices to God for the sins of the people, substituting the death of the animal for the death punishment deserved by the people for their sins and disobedience. This "substitution" brought an individual or a community back into a right relationship with God.
The Letter to the Hebrews shows how Christ took the place of the Mosaic priestly sacrifices once and for all. Just as in the Old Covenant the high priest would offer animal sacrifices on behalf of the people, so Christ became the new high priest who offered himself as the sacrificial offering for the sins of the people for all time. While the Old Covenant required ongoing sacrifices, Jesus' was once and for all, never to be repeated: "he entered once for all into the sanctuary, not with the blood of goats and calves but with his own blood, thus obtaining eternal redemption." (Hebrews 9:12)
The Catechism of the Catholic Church tells us that "Jesus' violent death was not the result of chance in an unfortunate coincidence of circumstances, but is part of the mystery of God's plan." (CCC 599) This is where the sense of paradox comes in: How could a loving and merciful God condemn his Son to such a fate? The only answer is love. God took the initiative to offer his Son on the cross in order to do something we could never do: save ourselves. Jesus took the punishment we deserved and became the instrument of atonement for our guilt to the Father. We are forgiven because of his suffering and death. This is why, for Catholics, the crucifix, in all its brutality, is the most powerful image of God's love and concern for each of us.