Matthew 2:4 After assembling all the chief priests and experts in the law, [Herod] asked them where the Christ was to be born. 2:5 “In Bethlehem of Judea,” they said, “for it is written this way by the prophet:
2:6 And you, Bethlehem, in the land of Judah,
are in no way least among the rulers of Judah,
for out of you will come a ruler who will shepherd my people Israel.’ ”

1. Some think that Matthew has deliberately reversed the meaning of the Micah text. 

Conner (All That’s Wrong With the Bible) asserts that Matthew’s version:

‘goes completely against the supposed prophecy by negating it.’

But such a summary dismissal of the text serves only to demonstrate the prejudice of the writer, who makes no attempt to understand what might be going on.

Turning to a reputable (if occasionally idiosyncratic) scholar, we find Gundry writing:

‘Matthew inserts “by no means” to deny emphatically the leastness of Bethlehem in Micah’s text. For Matthew, in other words, Jesus’ birth has transformed Bethlehem from the unimportant village it was during Micah’s time into the supremely important birthplace of the messianic king from David’s line.’

2. Others think that the meaning is essentially the same.

According to the 19th-century commentary by Jamieson, Fausset and Brown:

‘This quotation, though different verbally, agrees substantially with the Hebrew and LXX.  For says the prophet, “Though thou be little, yet out of thesee shall come the Ruler” – this honour more than compensating for its natural insignificance; while our Evangelist, by a lively turn, makes him say, “Thou art not the least: for our of thesee shall come a Governor” – this distinction lifting it from the lowest to the highest rank.”

Hendriksen:

‘Though the quotation from Mic. 5:2 is not according to the letter—the main change being the one from “who are little to be among” to “are by no means least among”—it is according to the essence, for in both cases the meaning is, “Though you, Bethlehem, are but little, yet you are by no means least, for Israel’s Ruler shall come forth from you.” As Micah saw it, therefore, and as the Jewish authorities now interpret it, Matthew concurring, in the tribal meetings where each city and village was represented by its chief or prince, Bethlehem, though small in population, is very important because Israel’s great Leader was destined to be born there.’

Geisler & Howe (When Critics Ask):

‘Matthew may be saying that since the Messiah is to come from this region, it is by no means least among the other areas of land in Judah. The phrase in Micah only says that Bethlehem is too little or small, as compared to the other areas of land in Judah. The verse does not say it is the least among them, only very little. Matthew is saying the same thing in different words, namely, that Bethlehem is little in size, but by no means the least in significance, since the Messiah was born there.’

Gundry notes (without giving references) that

‘Many have offered conjectural emendations of Micah’s text in order to assimilate it to Matthew’s, but the difficulty of the present text stands in its favour, and Matthews penchant for interpretation in quoting the OT militates against assimilation of Micah to Matthew.’

3. Others think that the ‘contradiction’ is formal, rather than material.  Matthew has changed the text in order to bring out its true meaning:

‘Matthew makes a key addition to Micah’s wording, by inserting the word translated “by no means,” to show that the fulfillment of this prophecy has transformed Bethlehem from a relatively insignificant town into a city of great honor. What seems at first glance to create a formal contradiction in fact involves an addition designed to make the text accurately reflect the altered situation. This combination of translation and commentary closely resembles that of the Jewish targums. Discerning Jewish readers would have known the wording of the original text and would have recognized that Matthew’s addition was not a mistake in quoting the Scriptures but an interpretative explanation.’ (NAC; France explains similarly)

The contributor to the Commentary on the New Testament Use of the Old Testament agrees that the ‘contradiction’ is formal, rather than real:

‘The addition of “by no means” creates a formal but not a material contradiction (Carson 1984: 88). Bethlehem was insignificant by worldly standards, but once it was graced with the birth of the Messiah, it was no longer insignificant, at least not by God’s standards.’

However, if this is the case, it is curious that Matthew seems to place these words in mouths of others.

Osborne:

‘Matthew has also added “by no means” (οὐδαμῶς), which formally contradicts Mic 5:2 (“though small among the clans of Judah”) but actually highlights the greatness that is the true meaning of the passage. Matthew is interpreting the text to emphasize that the insignificant village of Bethlehem has become truly great because the Messiah was born there.’

In Blomberg’s opinion, Matthew is using a well-known strategy of combining translation with commentary:

‘Matthew makes a key addition to Micah’s wording, by inserting the word translated “by no means,” to show that the fulfillment of this prophecy has transformed Bethlehem from a relatively insignificant town into a city of great honor. What seems at first glance to create a formal contradiction in fact involves an addition designed to make the text accurately reflect the altered situation. This combination of translation and commentary closely resembles that of the Jewish targums. Discerning Jewish readers would have known the wording of the original text and would have recognized that Matthew’s addition was not a mistake in quoting the Scriptures but an interpretative explanation.’

Hagner thinks that Matthew may be utilising a reading already current in his day:

‘Given Matthew’s sense of the fulfillment that has occurred in Bethlehem, the initial statement of the prophet must now paradoxically be reversed: hence, οὐδαμῶς ἐλαχίστη, “by no means the least.” But the change may involve more than simply a liberty on the evangelist’s part. If in the MT the initial ל were read as the negative particle (לאֹ, lōʾ) i.e. with the slight change of לִהְיוֹת, lihyôt, to לאֹהְיוֹת, lōʾhĕyôt, a reading is produced that coincides with Matthew’s Greek rendering of the passage. This reading, given its appropriateness in a reference to the birth of the coming ruler, could possibly already have been circulating in Matthew’s time.’

Hagner’s suggestion works well in the light of the fact (which many commentators overlook) that the words in question are placed in the mouths of ‘the chief priests and experts in the law’.