The debt part of the question:
What is a debt? Something you owe because you made an agreement to repay something. Also, something you owe because you took what is not yours, thus have something that is not yours but belongs to the person from whom you took it.
Sinning is like the second: The sin is taking and enjoying. The result is that the owner no longer has it nor enjoys it.
Long after the stealing, you still have in your soul the history of the enjoyment and satisfaction of your theft, you have both guilt and injustice. You have guilt (you are guilty of having done the sin), and injustice (you still possess the understanding of satisfaction from the use of what was stolen and the understanding that the satisfaction is missing from the life of the one from whom you stole it).
A sacrifice was meant to atone for the existing injustice, the imbalance of what belongs to whom. So you do without some satisfaction of your own (a spotless lamb from your flock which is worth many moments of future satisfaction to you that you will now not have when you give it up).
As for God, what do we steal from him? Life. We do all sorts of things and everything to make ourselves alive, happy, satisfied, to keep death and suffering far from ourselves. And we do not wait in patience to receive life and all good from God. We, like Adam and Eve, look at what appears good to consume and good for some physical benefit, and then take it and eat it. We do not remember God saying, “Here, eat from this tree, and this one, and also this one and that one, and do this and do that.” and then do what he says.
We have the satisfactions that don’t belong to us but not the ones he gives. How can we return our stolen life to God? One way would be by dying, but what value is there in returning stolen life, stolen from things he never intended to be life-giving? So we give “spotless lambs”, but we continue to steal, so we give them repeatedly. What can end the cycle? If we, ourselves, were alive from him, and never stole again, only one sacrifice would be needed. But what sacrifice can both return what was not ours and also make us new and virtuous? That is Jesus, who did both. He returned the satisfaction of life to God, his life that was not stolen (in the desert with Satan he did not satisfy his need of life by turning stones to bread, he did not satisfy his need to be king by worshipping Satan, and he did not satisfy his need to be sure of life by throwing himself from the temple pinnacle). He gave back to God what we stole, and it was satisfactory to God because he gave back real life, un-stolen life. His life was returned to him, and he shares it with us, giving us himself, his Spirit, his Father, in Baptism and in his presence with and in us. He gives us gifts, the Virtues, so that we may be like him. Our life now is perseverance in being like him: putting off the old nature that takes life for itself; seeking his Kingdom and his Goodness (righteousness); self-sacrifice so that others may have the goodness and life he gives; etc.