First the part that "got them going":
The explanation I was given went something like this. God was very angry with us for our sins, and because he is a just God, our sin had to be punished. But instead of punishing us he sent his Son, Jesus, as a substitute to suffer and die in our place. The blood of Jesus paid the price of our sins, and because of him God stopped being angry with us. In other words, Jesus took the rap, and we got forgiven, provided we said we believed in him.
Well, I don't know about you, but even at the age of ten I thought this explanation was pretty repulsive as well as nonsensical. What sort of God was this, getting so angry with the world and the people he created, and then, to calm himself down, demanding the blood of his own Son? And anyway, why should God forgive us through punishing somebody else? It was worse than illogical, it was insane. It made God sound like a psychopath. If any human being behaved like this we'd say they were a monster.
Well, I haven't changed my mind since. That explanation of the cross just doesn't work, though sadly it's one that's still all too often preached. It just doesn't make sense to talk about a nice Jesus down here, placating the wrath of a nasty, angry Father God in heaven. Christians believe Jesus is God incarnate. As he said, 'Whoever sees me has seen the Father'. Jesus is what God is: he is the one who shows us God's nature. And the most basic truth about God's nature is that He is Love, not wrath and punishment.
And then the "OK ... if that's not what the point of the cross is what IS the point?" part:
The cross, then, is not about Jesus reconciling an angry God to us; it's almost the opposite. It's about a totally loving God, incarnate in Christ, reconciling us to him. On the cross Jesus dies for our sins; the price of our sin is paid; but it is not paid to God but by God. As St Paul says, God was in Christ reconciling the world to himself. Because he is Love, God does what Love does: He unites himself with the beloved. He enters his own creation and goes to the bottom line for us. Not sending a substitute to vent his punishment on, but going himself to the bitter end, sharing in the worst of suffering and grief that life can throw at us, and finally sharing our death, so that he can bring us through death to life in him.
Fr. Jake has some commentary here ... always worth reading is Fr. Jake.