RELIGOUS THREAD (flashing sirens here)

So yeah, this is a question that has bothered me for pretty much all of my sentient life. It's a big part of the reason I stopped going to church. So, for all the Christians and amateur-theologians out there, I pose my eternal question:

How did the death of Jesus Christ help humanity?

Every answer I've heard for this is purely symbolic in nature - that his death was basically a sacrifice akin to the animal sacraments of the Hebrews, but since he was the son of God this absolved all sins for the rest of eternity. What I don't understand about this explanation though is why God would need to go through so much trouble and put his earthly embodiment through pain and torture in order to change his own mind about how things work.

This isn't a "your religion is illogical" thread. I am honestly trying to gain a better grasp here of the religion I grew up with and that is so dear to so many of my friends and family.

Jam it back in, in the dark.