I have just read your article on the Old Testament versus the New Testament. I find two major difficulties in your argument: 1) You confuse a covenant with the Law. This is a major mistake. The Law is God's legislation for all of creation. It was given to the children of Israel for their instruction. A covenant is an agreement between two parties. It is not the same as the Law. 2) The new covenant in no way changes the Law. It merely changes the agreement between God and man.
The article in reference is "Why We Don't Follow the Old Testament." I found this particular disagreement amusing because not long ago another person objected to the same article, but argued that the law changed and the covenant remained in place.
Let us tackle the first point. Does the Bible consider "law" and "covenant" to be two different things or two equivalent things? You later wrote in your note (not included), argues that the words translated "covenant" and "law" come from two different Hebrew words which have different meanings. Unfortunately this does not make your point. For example, the words "Messiah," "Jesus," and "Son of God" all have different meanings, yet all refer to the same individual. The reason is simple; no single word can adequately describe our Lord. Each word emphasizes a different aspect and, when combined, gives us a multi-dimensional view of the nature and character of Jesus. In the same fashion, God uses a variety of terms to describe the Mosaical Law. Consider this portion of Psalm 19:
The law of the LORD is perfect, restoring the soul;
The testimony of the LORD is sure, making wise the simple.
The precepts of the LORD are right, rejoicing the heart;
The commandment of the LORD is pure, enlightening the eyes.
The fear of the LORD is clean, enduring forever;
The judgments of the LORD are true; they are righteous altogether.
Is David talking about six different things or one thing described in six different ways? The answer is obviously the latter. The law, the testimony, the precepts, the commandment, the fear, and the judgments all refer to the same written document. You argue that the covenant has changed, but not the law. Hear what Moses said, "So He declared to you His covenant which He commanded you to perform, the Ten Commandments; and He wrote them on two tablets of stone. And the LORD commanded me at that time to teach you statutes and judgments, that you might observe them in the land which you cross over to possess" (Deuteronomy 4:13-14). Moses called the Ten Commandments God's covenant. Are you prepared to state that the Ten Commandments changed while the Law of Moses remained fix? Or consider Psalm 78:10, "They did not keep the covenant of God; They refused to walk in His law." In two parallel constructs "the covenant of God" and "His law" are used to refer to the same work.
The prophet Jeremiah spoke of a day when the covenant would change. "Behold, the days are coming, says the LORD, when I will make a new covenant with the house of Israel and with the house of Judah - not according to the covenant that I made with their fathers in the day that I took them by the hand to lead them out of the land of Egypt, My covenant which they broke, though I was a husband to them, says the LORD. But this is the covenant that I will make with the house of Israel after those days, says the LORD: I will put My law in their minds, and write it on their hearts; and I will be their God, and they shall be My people" (Jeremiah 31:31-33). Notice the change in terms, God would give a new covenant to His people, writing His law on their hearts.
The writer of Hebrews does the same interchange of terms.
"For on the one hand there is an annulling of the former commandment because of its weakness and unprofitableness, for the law made nothing perfect; on the other hand, there is the bringing in of a better hope, through which we draw near to God" (Hebrews 7:18-19).
"But now He has obtained a more excellent ministry, inasmuch as He is also Mediator of a better covenant, which was established on better promises. For if that first covenant had been faultless, then no place would have been sought for a second" (Hebrews 8:6-7).
"In that He says, "A new covenant," He has made the first obsolete. Now what is becoming obsolete and growing old is ready to vanish away" (Hebrews 8:13).
"And for this reason He is the Mediator of the new covenant, by means of death, for the redemption of the transgressions under the first covenant, that those who are called may receive the promise of the eternal inheritance. For where there is a testament, there must also of necessity be the death of the testator. For a testament is in force after men are dead, since it has no power at all while the testator lives. Therefore not even the first covenant was dedicated without blood. For when Moses had spoken every precept to all the people according to the law, he took the blood of calves and goats, with water, scarlet wool, and hyssop, and sprinkled both the book itself and all the people, saying, "This is the blood of the covenant which God has commanded you" (Hebrews 9:15-20).
"For the law, having a shadow of the good things to come, and not the very image of the things, can never with these same sacrifices, which they offer continually year by year, make those who approach perfect" (Hebrews 10:1).
"Previously saying, "Sacrifice and offering, burnt offerings, and offerings for sin You did not desire, nor had pleasure in them" (which are offered according to the law), then He said, "Behold, I have come to do Your will, O God." He takes away the first that He may establish the second" (Hebrews 10:8-9).
Commandment, testament, law, precept, and covenant all refer to the same thing. These verse also clearly state that there was a change in the Law because the Law was unable to save mankind. Hence the first Law was removed in order to establish the second. This is precisely the same point Paul made in Romans (and notice Paul's use of the word "law"). "Therefore, my brethren, you also have become dead to the law through the body of Christ, that you may be married to another--to Him who was raised from the dead, that we should bear fruit to God. For when we were in the flesh, the sinful passions which were aroused by the law were at work in our members to bear fruit to death. But now we have been delivered from the law, having died to what we were held by, so that we should serve in the newness of the Spirit and not in the oldness of the letter. What shall we say then? Is the law sin? Certainly not! On the contrary, I would not have known sin except through the law. For I would not have known covetousness unless the law had said, "You shall not covet." But sin, taking opportunity by the commandment, produced in me all manner of evil desire. For apart from the law sin was dead" (Romans 7:4-8). Recall that Moses referred to the Ten Commandments as God's covenant. Here Paul discusses the removal of the Law and uses the tenth commandment of the Ten Commandments as an illustration of why that Law did not save.
The same point is made in Ephesians, "Therefore remember that you, once Gentiles in the flesh--who are called Uncircumcision by what is called the Circumcision made in the flesh by hands-- that at that time you were without Christ, being aliens from the commonwealth of Israel and strangers from the covenants of promise, having no hope and without God in the world. But now in Christ Jesus you who once were far off have been brought near by the blood of Christ. For He Himself is our peace, who has made both one, and has broken down the middle wall of separation, having abolished in His flesh the enmity, that is, the law of commandments contained in ordinances, so as to create in Himself one new man from the two, thus making peace, and that He might reconcile them both to God in one body through the cross, thereby putting to death the enmity. And He came and preached peace to you who were afar off and to those who were near. For through Him we both have access by one Spirit to the Father. Now, therefore, you are no longer strangers and foreigners, but fellow citizens with the saints and members of the household of God, having been built on the foundation of the apostles and prophets, Jesus Christ Himself being the chief cornerstone" (Ephesians 2:11-20).
It is true that Jesus stated, "Do not think that I came to destroy the Law or the Prophets. I did not come to destroy but to fulfill. For assuredly, I say to you, till heaven and earth pass away, one jot or one tittle will by no means pass from the law till all is fulfilled" (Matthew 5:17-18). Jesus did not state that the law would never end. He promised that it would not end until it was fulfilled. He told the disciples the same in Luke 24:44, "Then He said to them, "These are the words which I spoke to you while I was still with you, that all things must be fulfilled which were written in the Law of Moses and the Prophets and the Psalms concerning Me."" The reason Jesus died on the cross was to fulfill the Law. And this Christ did. "For Christ is the end of the law for righteousness to everyone who believes" (Romans 10:4). Jesus was the goal of law. He was the reason for its existence. He fulfilled all its promises and thus He brought it to an end in order to establish a new Law built on better promises.