Simply, God has a sense of justice that must be satisfied one way or another. He hates our sin so much that only bloodshed can atone for it. But because He also loves us, He was willing to shed His own Son's blood instead of ours.
That's basic Christian theology -- if you don't understand it, then you have no grasp of Christianity.
He [God] hates our sin so much that only bloodshed can atone for it.
Answers the qeustion:
Please explain how suffereing "pays" for anything, and why God is so eager to accept "pain" as a payment.
Now, you may be right, "That's basic Christian theology -- if you don't understand it, then you have no grasp of Christianity," even though I have studied "Christian theology," for over forty years," but, if the above is your answer to the question asked, you have no grasp of simple logic, because it does not answer anything at all.
I suggest you look at MarMema's excellent post here and the link provided. I assure you, MarMema is an excellent student of theology.
Hank