Sometimes, when comparing New Testament citations of Old Testament passages, there are apparent differences in the text. These instances can be troubling for those who lack a framework for interpreting them. For instance, Matthew cites Mic 5:2-4 thus,
‘And you, O Bethlehem, in the land of Judah, are by no means least among the rulers of Judah; for from you shall come a ruler who will shepherd my people Israel.’ (Mt 2:6, ESV)
The original text of Mic 5:2-4, however, includes much more detail:
But you, O Bethlehem Ephrathah, who are too little to be among the clans of Judah, from you shall come forth for me one who is to be ruler in Israel, whose coming forth is from of old, from ancient days. 3 Therefore he shall give them up until the time when she who is in labor has given birth; then the rest of his brothers shall return to the people of Israel. 4 And he shall stand and shepherd his flock in the strength of the LORD, in the majesty of the name of the LORD his God. And they shall dwell secure, for now he shall be great to the ends of the earth. (ESV)
Did Matthew misquote Micah? Not at all.
In such cases, we have to distinguish the writer’s intention. Was it to quote the text verbatim? Or simply to relate the gist of a text? Matthew’s audience was mostly Jewish and had access to the Scriptures. He therefore simply gives Micah’s main point in his own words. This was not extraordinary and would have been understood.
Calvin elaborates this principle very well, I think:
The scribes quoted faithfully, no doubt, the words of the passage in their own language, as it is found in the prophet. But Matthew reckoned it enough to point out the passage; and, as he wrote in Greek, he followed the ordinary reading. This passage, and others of the same kind, readily suggest the inference, that Matthew did not compose his Gospel in the Hebrew language. It ought always to be observed that, whenever any proof from Scripture is quoted by the apostles, though they do not translate word for word, and sometimes depart widely from the language, yet it is applied correctly and appropriately to their subject. Let the reader always consider the purpose for which passages of Scripture are brought forward by the Evangelists, so as not to stick too closely to the particular words, but to be satisfied with this, that the Evangelists never torture Scripture into a different meaning, but apply it correctly in its native meaning.
— John Calvin and William Pringle, Commentary on a Harmony of the Evangelists Matthew, Mark, and Luke, vol. 1 (Bellingham, WA: Logos Bible Software, 2010), 133–134.
In his commentary, R. T. France presents a similar take on Matthew’s use of Micah, and then observes how even today, preachers often do something similar in how we handle Scripture:
The whole point of Micah’s mentioning Bethlehem’s insignificance was by way of contrast to the glory it was to achieve as the birthplace of the Messiah; now Matthew can claim that that glory has come to Bethlehem, so that it is no longer the least (and the addition of “for” to introduce the next clause underlines the point). Rather than add a footnote, Matthew has incorporated the fulfillment into the wording of the text. For those who are familiar with the original text the alteration will stand out as a challenge to think through how Matthew’s story relates to the prophetic tradition. In a number of ways, therefore, Matthew has adapted Micah’s words to suit what he can now see to be their fulfillment, and to advance his argument for the scriptural justification of the Messiah’s origins.
This relatively free and creative handling of the text (not unlike that found in contemporary Aramaic targums) differs little from the practice of many modern preachers who, if not reading directly out of the Bible, will often (probably quite unconsciously) quote a text in an adapted form which helps the audience to see how the text relates to the argument. No-one is misled, and the hermeneutical procedure is well understood. Micah’s words have been applied appropriately, even if not with the literalistic precision which the age of the printed Bible makes possible.
— R. T. France, The Gospel of Matthew, The New International Commentary on the New Testament (Grand Rapids, MI: Wm. B. Eerdmans Publication Co., 2007), 73.
So, there you have it. New Testament writers don’t misquote the Old Testament. But sometimes they summarize, connect, and interpret the passages they interact with. What matters is that they are faithful to the sense intended by the Holy Spirit.