Mount Sinai covenant = bondwoman = slaves = cast it out....
Actually, you are correct here.
The Old Covenant was a physical covenant that was made with a physical people. They did not have access to the Holy Spirit and therefore the promises made to them were physical...
Lev 18:5 Ye shall therefore keep my statutes, and my judgments: which if a man do, he shall live in them: I am the LORD.
The promises were individual and national blessings of a temporal nature.
The New Covenant is a spiritual covenant based on Spiritual PROMISES...
Heb 8:6 But now hath he obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises.
Note carefully, that the N.C. was based on better PROMISES. The Laws are the same...
Heb 8:8 For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:
Heb 8:9 Not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my covenant, and I regarded them not, saith the Lord.
Heb 8:10 For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
Heb 8:11 And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.
Nothing is ever said about giving new and better Laws. What is given is the Holy Spirit which gives one the ability to understand not only the letter of the Law but the Spirit of the Law and then to LIVE BY THE SPIRIT OF THE LAW.
The Law itself is never listed as the problem...
Rom 7:12 Wherefore the law is holy, and the commandment holy, and just, and good.
Rom 7:14 For we know that the law is spiritual: but I am carnal, sold under sin.
This verse nails the problem. The problem is a carnal heart cannot live as God wants him to...
Rom 8:7 Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be.
Rom 8:8 So then they that are in the flesh cannot please God.
Same problem Israel had...
Heb 8:8 For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:
What was the fault He found with them?
Jer 31:32 Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt;
which my covenant they brake, although I was an husband unto them, saith the LORD:
Heb 3:10 Wherefore I was grieved with that generation, and said, They do alway err in their heart; and they have not known my ways.
The Holy Spirit gives one the ability to have the Law imprinted on his heart and mind...
Jer 31:33 But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.
With the Holy Spirit one can KNOW the mind of God...
Rom 8:9 But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his.
Jer 31:34 And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
Heb 8:11 And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.