Many Christians will point to Hebrews 8 to show that “the Old Covenant” was abolished at the cross.
Hebrews 8:7. For, if the first (covenant) had been faultless, there would have been no place for this second (one). 8. For he rebukes them and says: Behold the days come, says Master YHWH, when I will complete with the family of the house of Israel and with the family of the house of Yehuda, a renewed covenant; 9. not like the covenant which I gave to their fathers in the day when I took them by the hand and brought them out of the land of Egypt; (and) because they continued not in my covenant, I also rejected them, says Master YHWH.
10. But this is the covenant which I will give to the family of the house of Israel after those days, says Master YHWH: I will put my Torah in their minds and inscribe it on their hearts; and I will be to them a Elohim, and they will be to me a people. 11. And one will not teach his son of the city nor his brother, nor say: You shall know your Master YHWH: because they will all know me, from the youngest of them to the oldest. 12. And I will forgive them their iniquity; and their sins will I remember no more. 13. In that he said a Renewed (Covenant), he made the first old; and that which is old and decaying, is near to disappearing.
Employing a Hebraic mindset (rather than a "Greek" one) let’s take a look at this passage using footnotes from the Aramaic English New Testament by Andrew Gabriel Roth:
 Most Christians seem to forget that without the first covenant, the second one is impossible! In very short order Rav Shaul will quote Jeremiah 31:31-34, indicating that the Renewed Covenant is a contingency triggered by, and deriving authority from, the first covenant. YHWH declared that the Ancient Covenant He made with Israel was good; it was to bring life, but the people of Israel chose to willfully break this Covenant and treat it as a vain thing. See Deuteronomy 32:46, 47.
 Paul makes reference to the Renewed Covenant (Jeremiah 31:31-34) nine times in this letter.
 The phrase in Aramaic is 'bar medintheh', which literally means “son of his city” but idiomatically carries the meaning of “fellow citizen, neighbor” and most definitely a metaphor Greek does not have. This fact puts Peshitta well before the end of the Second Century when the mistranslated Greek texts were done. It is also important to note that this is the last book of the Eastern canon. As a result, the entire collection must have circulated prior to this very early date.
 The context is Jeremiah 31:31-34, what is “near to disappearing” is the sinful nature of man that breaks Torah, not the standard of Torah. Remember that we broke Torah, not YHWH. YHWH did not drop the standard of Torah because Israel chose disobedience; rather, He installed a Renewed Covenant to write Torah upon the heart through the work of the Ruach haKodesh, according to Mashiyach. The fact of the matter is that in Mashiyach, YHWH raised the bar; He magnified Torah; see Isaiah 42:21. Because mankind broke Covenant, YHWH requires complete renovation on our part, not YHWH’s part of the Covenant. This verse in its twisted form, became one of the “crown jewels” of Torahless Christianity which teaches that Torah is decaying and is near to disappearing, but nothing could be farther from the truth. See 2 Peter 3:16.