This is probably more than most of ya'll can see,but did you know that God used Abraham and His covenant with Abraham to bring Jesus into the earth and to have the right to sacrifice him? I'm sure that one will leave most saying, WHAT!
Yes. The account of God entering into covenant with Abraham is the most fascinating thing and a huge key to understanding the Bible. The significance of a blood covenant is lost on modern people because we don't have them anymore. We have paper contracts which when broken we take to court and attempt to take the offending party's money. In ancient times, the breaking of a blood covenant was a death penalty. This is why God had every right to wipe Israel out on many occasions when they violated it and his mercy in the OT is underrated.
In a nutshell, think of a blood covenant as portrayed by old westerns where an Indian and a white guy would cut each other's palms, bring them together and become "blood brothers". Its a gross oversimplification but at least a place to start.
The account of God's covenant with Abraham is in Genesis 15. God had made promises to Abraham concerning his descendants and land. While we know Abraham "believed God" he asked him "how can I know" that I will inherit all these things. God's response was "bring me a heifer, a goat, a ram and two pigeons". Abraham brought these animals, killed them, and split them in half down the back. God didn't tell him to do that but it must have just been the way things were done in those days. God's response to Abraham was the ancient version of "lets have papers drawn up".
God passed between the pieces of animals as said in Genesis and "swore by himself" his promises to Abraham binding himself to Abraham in a blood covenant. Essentially saying if he broke it, let what happened to the animals happen to him.
Parties in covenant with each other have right to everything the other party has. God asked Abraham for his son and Abraham obliged. As you say, this gave God the right, or perhaps the obligation to offer his.
The only other reference to cutting animals in half in the bible to my knowledge is Jeremiah 34:18. The concept of covenant winds its way through the entire Bible.
Very deep subject. Bigly deep.
