It seems there is some study to be done on the new and Old Covenant.
Yes there are two.
Yes one is done away with.
To this extent most are right, its how they then conclude that is often erroneous.
For example. The New Covenant says:
Rom_13:10 Love worketh no ill to his neighbour: therefore love is the fulfilling of the law.
and the Old Covenant said:
Lev_19:18 Thou shalt not avenge, nor bear any grudge against the children of thy people, but thou shalt love thy neighbour as thyself: I am the LORD.
Notice they are the same, Love your neighbour.
The error people make is this, They think the new covenant reinstated this, but that is not true it never changed. The covenant changed from old to new, but the law to love our neighbour remained through both.
Jesus did not die to change love your neighbour so the teaching remained as it has always been true that God expects us to love our neighbour. As He did before the law was given through Moses.
See the new testament is simply a quote the Old is where it is quoted from and is the first witness. It is From the Old testament that this quote to love your neighbour gets its authority as it is written:
2Ti 3:16 All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:
2Ti 3:17 That the man of God may be perfect, throughly furnished unto all good works.
Of course when this was written there was not new testament and thus it is in fact the Old Testament with the Old Covenant that is profitable for doctrine for reproof etc.
Jesus and the disciples taught from the Old Covenant.
In fact it is the Old covenant that teaches that circumcision is of the heart:
Deu_10:16 Circumcise therefore the foreskin of your heart, and be no more stiffnecked.
Deu_30:6 And the LORD thy God will circumcise thine heart, and the heart of thy seed, to love the LORD thy God with all thine heart, and with all thy soul, that thou mayest live.
Jer_4:4 Circumcise yourselves to the LORD, and take away the foreskins of your heart, ye men of Judah and inhabitants of Jerusalem: lest my fury come forth like fire, and burn that none can quench it, because of the evil of your doings.
This is how they came to the conclusion that it was no longer important as Deut 30 shows this would apply after they were brought back from captivity. and in connection with the new covenant.
You can prove from the old testament the end of sacrifices and the temple service on earth.
In fact you can just about preach every teaching found in the new testament without using the new testament but the Old.
One does not replace the other. One testifies to the validity of the Other. The new testament proves the first and validates its prophetic utterances. that is why Jesus said, "it is written" "have you not read" "you are in error not knowing the scriptures" "what is written in the law", and of course the fact that he often quotes the Old Testament in His teachings. Gets his parables from the Old Testament. and Knew his mission form the Old Testament.
Blessings.