Was Jesus sent to be crucified?
That is one, and seems the predominating reason for the Incarnation, one that presents an angry God demanding payment for sin. There is an alternative interpretation to 'why Jesus.?'
It holds that the whole purpose of creation is for the Incarnation, God's sharing of life and love, God becoming human is not an afterthought, a plan b, an event to make up for Original sin and human sinfulness. Incarnation is God's first thought, the original design for all creation. The purpose of Jesus' life is the fulfillment of God's eternal longing to become human. John's Gospel does not see Jesus' death as a ransom, nor is there the language of sacrifice, atonement. The emphasis is on intimacy, service, faithful love, revealing God's desire and gift for humanity, salvation. In John the crucifixion is the "hour" of glorification, not sacrifice but epiphany, the manifestation of God. For John the reality is a God who wants to share divine life.
The question, would the Son of God have become incarnate if humanity had not sinned? The answer from one philosopher, theologian, Thomas Aquinas was no, the Incarnation was a remedy for sin. The alternative view is presented by Franciscan John Duns Scotus, another philosopher and theologian. He based his view on the Scriptures and early theologians, and divine love. I once stated that formulations, dogmas, doctrine, are time conditioned. The Church originally condemned this theology of Scotus, he is now know as and given the title of Blessed John Scotus.
A few years ago there was a German Archbishop who found himself on the receiving end of conservative outrage. Bishop Zollitsch had stated that Christ "did not die for the sins of the people as if God had provided a sacrificial offering like a scapegoat." Instead, Jesus had offered only "solidarity" with the poor and suffering, that is this great perspective, this tremendous solidarity."