God's covenant with Abraham is the foundation of God's Covenant of Grace.
Genesis 17:1:
The Covenant and Its Sign.
When Abram was ninety-nine years old, the Lord appeared to him and said, “I am God Almighty. Walk before me and be blameless. I will establish my covenant between me and you and I will multiply you greatly.”
When God told Abraham to "Walk before me and be blameless" he is telling Abraham that he has the power and authority to forgive transgressions and if Abraham walks before him (follows him) he will be held blameless.
Genesis 3:
Abram immediately fell down upon his face. God said to him, 4“On my part, behold, my covenant with you: you will be the father of many nations. 5. You will no longer be called Abram, but Abraham, for I will make you the father of many nations. I will make you very, very fruitful. I will make nations come from you, and you shall give birth to kings. 7. I will establish my covenant with you for all generations. It will be an eternal covenant. I will be your God and the God of your descendants after you. 8. I will give you and your descendants after you this land where you are now an alien. All of the land of Canaan shall be your eternal possession. I will be your God.”
When God states, "I will be your God" that means Abraham and his descendants fall under his direct authority - which includes his authority to hold them "blameless" as long as they "walk before him" and fulfill their part of the covenant.
Genesis 9:
God said to Abraham, “On your part, you must observe my covenant, you and your descendants after you, for all time. 10.This is my covenant that you must observe, a covenant between me and your descendants after you: every male among you must be circumcised. 11. You shall circumcise the flesh of the male member. This shall be the sign of the covenant between me and you.
God states that "Every male among you must be circumcised". Then goes on to state, "You shall circumcise the flesh of the male member. This shall be the sign of the covenant between me and you."
Does God seemingly repeat himself here? No, I do not believe so. We can get a better understanding of how God regarded circumcision from Deuteronomy 12-19:
God’s Steadfast Love.
And so now, O Israel, what does the Lord, your God, require of you but to fear the Lord, your God, to walk in all of his ways, to love him, to serve the Lord, your God, with all your heart and all your soul, 13 and to observe the commandments and the statutes that I am giving you today for your own good. 14: Indeed the heavens and the highest heavens belong to the Lord, your God, as well as the earth and all that is in it, 15. yet the Lord’s sole delight was in your fathers. He loved them so much that he chose you, their descendants, above every other nation, which is still true today.
16. Therefore, circumcise the foreskin of your hearts, and stop being stiff-necked, for the Lord, your God, is the God of gods and the Lord of lords, a great God, mighty and awesome, who does not show partiality nor take a bribe. 18 He ensures justice for the orphan and the widow, and demonstrates his love for the foreigner by giving him food and clothing. 19 So now, show your love to the foreigner, for you were once foreigners in the land of Egypt.
Circumcision was considered both a Spiritual sacrifice and physical sacrifice. Spiritually, one had to "circumcise the foreskin of their hearts - which led to humility and trusting that if they followed God's commands, and held true to his covenant, God's grace would break their yolks of oppression - allowing them to no longer be "stiff necked."
Genesis 12:
Whenever baby boys are eight days old, they will be circumcised, whether they are your own children or the children of those whom you bought and who are foreigners and not of your bloodline. 13. You must circumcise those who are born in your house and those who are bought by you. Thus, my covenant will be marked in your flesh as an eternal covenant. 14. The male who is not circumcised, the one whose flesh of his member is not circumcised, is to be cut off from his people. He will have violated my covenant.”
To many, this passage could sound like a strict, "Old Testament" commandment. The reality is, this was God giving the gift of his Grace not only to Abraham and his bloodline but also to anyone "who is born in or brought into their house" - including foreigners.
The physical act of circumcision was "the symbol" of the covenant - not the covenant itself. For one could be physically circumcised but if they did not "circumcise the foreskins of their hearts" and follow God's ways, they would not fulfill God's covenant.
As others have pointed out - the physical act of circumcision helped a great deal in the health and sanitation of men (and women by spreading less disease) during those times. Most men would likely not have known this so for them, it truly was a sacrifice and act of faith. In my opinion, this demonstrates how God works in mysterious ways with us at times - but in the end, proves to have our best interests at heart.
Genesis 17:
17.;Abraham bowed down to the earth and laughed when he thought, “Shall a man who is one hundred years old have a son? And Sarah, who is ninety years old, can she give birth?” 18 Abraham said to God, “If only Ishmael might live in your presence!”
19. But God said, “No, but Sarah, your wife, shall bear you a son, and you shall name him Isaac. I will establish my covenant with him as an eternal covenant, that I will be his God and the God of his descendants after him. 20. As for Ishmael, I have heard you. Behold, I will bless him and make him fruitful and very, very numerous. Twelve princes shall come from him and I will make him a great nation. 21. But I will establish my covenant with Isaac. Sarah shall give birth to him by this time next year.” 22. God thus finished speaking to Abraham, and rising into the heavens, he left him.
This further solidifies the fact that this was a very special covenant of grace - given by God to Abraham and his descendants. Although God would still bless Ishmael and his descendants, making them fruitful - he established this specific eternal covenant only with Abraham and Isaac and his descendants. The Israelites (descendants of Isaac) would be under God's authority and the requirements and benefits (Grace) associated with it.
In regards to the writings of Paul on the issue - Paul and the Apostles were under a significant amount of persecution from both the Jewish leaders and Rome at the time. Paul was teaching a very Spiritual form of Jesus' teachings - to the extent that both he and Peter had disagreements at times. In reference to the Spirit opposing the flesh and vice versa - Paul is spot on, in my humble opinion.
In my opinion, the idea is that Jesus also taught us how to live lives within society - even under the law as long as we held true to his two most important teachings - to love God with all your heart, soul and mind and to love your neighbor as yourself. If we followed those two teachings, most of the major teachings and laws would naturally fall into place. If we are clean in mind and Spirit - we would more than likely also be clean in the flesh.
Let's remember that Jesus "Did not come to abolish the teachings of the Prophets and Law but to fulfill it". Although many might not see it, God's grace was evident in the books of the Old Testament. Jesus was well aware of it - he quoted it and spoke of it regularly.
Luke 17:
20. The Coming of the Kingdom of God.
Once, the Pharisees asked him when the kingdom of God was coming. He answered, “The coming of the kingdom of God will not occur with signs that can be observed. 21. Nor will people say, ‘Here it is,’ or ‘There it is.’ For the kingdom of God is in your midst.”
To finish - Catholics (and many Christians) pray "In the Name of the Father, Son and Holy Spirit". It represents the Holy Trinity and through it - can also represent the balance we should seek in life, in my opinion. Mind - Body and Spirit - and instead of one being opposed to the other - we can acknowledge their differences but always strive for balance (mind), moderation (flesh) and humility (Spirit).