Is the flaw of the Old Covenant (Hebrews 8:7) that there was no way for sins to be completely forgiven (Hebrews 10:1-10)? Or was the law impossible to completely follow as well? If it was possible to completely follow, then what is Peter talking about in Acts 15:10 and what is the meaning of Hebrews 7:18-19? I ask because a member told me that she did not believe that God would give men a law (the Old Covenant) that could not have been kept; therefore, she thought it to not have had any fault.
All law, by its very nature, will be broken. People have free choice and once a choice is defined, there will be people who while make the wrong choice. Consider the law that God gave Adam and Eve, to not eat the fruit of the Tree of the Knowledge of Good and Evil. It was a simple law. Given that the tree was in the middle of a garden with every other kind of fruit tree available (Genesis 2:9), it ought to have been easy to keep this law. Yet, we know that the law was broken. See "The Nature of Law" for further details.
It is even true today with the Law of Christ. "If we say that we have no sin, we deceive ourselves, and the truth is not in us. ... If we say that we have not sinned, we make Him a liar, and His word is not in us" (I John 1:8, 10). Sure, in theory law can be kept, but in practice only Jesus Christ ever kept the law of God perfectly. The rest of mankind have been guilty of breaking God's laws.
What made the Old Law particularly difficult was that it offered no solution to the problem of sin beyond the promise that God would take care of it in the future. "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). That was the problem that Paul addressed:
"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. I was alive once without the law, but when the commandment came, sin revived and I died. And the commandment, which was to bring life, I found to bring death. For sin, taking occasion by the commandment, deceived me, and by it killed me. Therefore the law is holy, and the commandment holy and just and good. Has then what is good become death to me? Certainly not! But sin, that it might appear sin, was producing death in me through what is good, so that sin through the commandment might become exceedingly sinful. For we know that the law is spiritual, but I am carnal, sold under sin" (Romans 7:5-14).
Thus, your friend is wrong. The Old Law had a fault. "For if that first covenant had been faultless, then no place would have been sought for a second. Because finding fault with them, He says: "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 when I took them by the hand to lead them out of the land of Egypt; because they did not continue in My covenant, and I disregarded them, says the LORD" (Hebrews 8:7-9). The flaw wasn't directly in the law -- that was perfect as it came from God. But the law depended on man keeping it, which man proved unable to do; thus, proving we needed God's help. Really the fault was in man, not God.
The New Law is different. It still condemns sin and we still violate that law, but it offers a solution to the problem. "O wretched man that I am! Who will deliver me from this body of death? I thank God -- through Jesus Christ our Lord! So then, with the mind I myself serve the law of God, but with the flesh the law of sin" (Romans 7:24-25). Jesus' sacrifice allows us to escape sin. "My little children, these things I write to you, so that you may not sin. And if anyone sins, we have an Advocate with the Father, Jesus Christ the righteous. And He Himself is the propitiation for our sins, and not for ours only but also for the whole world" (I John 2:1-2).
The reason we reject going back under the Old Law, as Peter said, "Now therefore, why do you test God by putting a yoke on the neck of the disciples which neither our fathers nor we were able to bear?" (Acts 15:10), is because it would mean rejecting the solution to sin. Salvation is only truly available through the New Law and Christ. "Nor is there salvation in any other, for there is no other name under heaven given among men by which we must be saved" (Acts 4:12).