These differing reasons are what Catholics believe?
The latter is the favorite of the Franciscans.
Throughout the centuries, Christian theology and piety have developed these interpretations of Jesus' execution. At times God has even been described as demanding Jesus' suffering and death as a means of atonement—to satisfy and appease an angry God. In many forms of theology, popular piety and religious practice, the purpose of Jesus' life is directly linked to original sin and all human sinfulness. Without sin, there would have been no need for the Incarnation.
From this perspective, God is appreciated with a different emphasis. God is not an angry or vindictive God, demanding the suffering and death of Jesus as a payment for past sin. God is, instead, a gracious God, sharing divine life and love in creation and in the Incarnation (like parents sharing their love in the life of a new child). Evidently, such a view can dramatically change our image of God, our celebration of Christmas, our day-by-day prayer.
"In the beginning was the Word, and the Word was with God, and the Word was God....All things came to be through him, and without him nothing came to be....And the Word became flesh...." The Prologue of John's Gospel (1:1-18) gives us this magnificent vision, proclaiming that all creation came to be in the Word, God's self-expression who became flesh, Jesus.
John's meditation on God's supreme act of love in the Incarnation (also see 3:16) has led some theologians to consider that this event alone was sufficient to save the world. Indeed, John's Gospel does not see Jesus' death as a ransom (unlike the synoptic Gospels, for example, Mark 10:45), nor does it use the language of sacrifice or atonement. There is, instead, emphasis on friendship, intimacy, mutuality, service, faithful love—revealing God's desire and gift for the full flourishing of humanity, or in other words, salvation (see the Farewell Address, John 13:1—17:26).
Jesus' crucifixion (usually described as being "lifted up") is part of his "hour" of glorification, which also includes his resurrection and ascension. For John, this hour is not sacrifice but epiphany, the manifestation of God.
Hundreds of years later, in the Middle Ages, the question about Jesus was expressed very explicitly: Would the Son of God have become incarnate if humanity had not sinned? The great theologian St. Thomas Aquinas (1225-1274) answered in the negative, viewing the Incarnation as a remedy for sin.
Another great philosopher and theologian, Franciscan John Duns Scotus (1266-1308), disagreed with Thomas's emphasis on sin. Indeed, Duns Scotus boldly proclaimed and defended the primacy of the Incarnation. He based his view on the Scriptures and early theologians and on logic. He argued, for example, that God's supreme work, the Incarnation, had to be first and foremost in God's mind. It could not be dependent on or occasioned by any action of humans, especially sin.
I quoted from an article in the original periodical 'St Anthony's Messenger' which was sold and I cannot trace to the old site. I saved the original article but its a bit much to copy and paste.