It's safe to say that the orthodox Judeo-Christian view of remission of sin is that something must be sacrificed, a blood offering must be made, to appease God's wrath or stay His judgment. I've never really quibbled with the truth of that, but I've never quite understood why that is the case. Couldn't He accept us doing jumping jacks or cartwheels as acts of repentence? Couldn't the giving of alms take the place of the physical sacrifice of either an animal, under the Judaic cultic practices, or a Man, i.e. the crucifixion of Jesus, God incarnate? After all, God is God, right? He could accept any mode or act in remission of sin. Or could He.
There's an incredible amount of theological and philosophical study on this issue. I don't claim to know what most of the great minds think about it. I don't claim to have new thoughts, but only thoughts or ideas new to me.
Like my fellow modern man, my personal inclination is to say that there's something incredibly cruel, even wrong, about killing an animal -- to say nothing of a sinless God-Man -- to appease God's anger at my sins. It seems unjust in a way. I don't fault skeptics for finding it so, but I, through faith, trust that God's plans and ways are better than any of which I could possibly conceive.
It must be remembered that the sacrifice rituals performed as laid out in Exodus and Leviticus were nothing like vicious acts of bloodlust. While it's true a spotless (innocent) animal died in the process, the offered animal was eaten by the priests. Understanding that, only vegetarians and vegans would be left to say that no justification, whatsoever, for the sacrifice could be made on modern terms.
While it is hard to come to grips with its unpleasantness, its ugliness (again, to our modern way of viewing things), I see that is precisely why ritualistic sacrifice might have had to occur. Certainly modern people would be troubled that their wrongdoing cost a cute little lamb its life. If I knew something had to die to clean up the mistakes I made, and that this process would need to be repeated as my sins piled up, I might be more hesistant to err. I might be more willing to exercise discipline, to try to flee temptation. I might take more seriously my faults.
What would seem more unjust than to kill an innocent man for the crimes of another? To us, there is not much we would find more appalling. Yet, that is the lesson of the cross. Someone else was tortured to death for your lies, lust, anger, violence, cruelty, pettiness, impatience, gluttony, or hatred.
You might be man or woman enough to live out your life according to your own will if you knew that only you would have to account for that. That might seem contrary to our selfish natures, but I've heard many people in my life say they didn't mind the idea of Hell. They say, half jokingly, half seriously, "Oh, what does it matter, I'm going to Hell anyway!"
But consider that, to make up for those shortcomings, someone else had to die. What if someone else already died a horrible death to clean up your mess? Would knowing that cause you pause to examine your life?
Roman Catholics believe that Jesus' crucifixion is -- and this is my way of explaining it -- re-enacted in the Mass and that Jesus daily presents His crucified body before the Father to stay His judgment, to cover your sins. If that is the case, you can't be content to say, "Well, He already died and we no longer sacrifice animals so this is taken care of."
Ultimately, a blood sacrifice is a deterrent. It's a wake up call. You already have your own soul to account for; do you want another's blood on your hands as well?