And it does.
But it's not a specific individual prophecy that he is referring to.
The beginning of understanding is what Dog says here:
"Had Matthew intended to cite an exact prophetic quotation from the Old Testament, he would have cited a specific prophet, instead of saying summarily, as he does, “the prophets”.
Beautiful.
Mathew used the phrase, “through the prophet(s)”, more than anyone.
Only one time did he use the plural version; "This fulfilled what the prophetS had said.
Maybe not.
All that it means is, it could NOT be BETHLEHEM, EGYPT or RAMAH.
In the translation you quote:
"So the family went and lived in a town called Nazareth. This fulfilled what the prophets had said: “He will be called a Nazarene.”
We see the quotes around “He will be called a Nazarene.”
But not all translations have that:
"Then he went and settled in a town called Nazareth to fulfill what was spoken through the prophets, that He will be called a Nazarene. - CSB
And some don't even have the "that", that He will be called a Nazarene:
"And he came and dwelt in a city called Nazareth: that it might be fulfilled which was spoken by the prophets, He shall be called a Nazarene. - KJV
Don't forget that the translators put the punctuation in.
It could have been read like this:
"And he came out of Egypt and dwelt in a city called Nazareth that it might be fulfilled which was spoken by the prophets. He shall be called a Nazarene.
And since Mathew uses the plural, we know he's not talking about one single prophet or prophecy.
I'm sure, considering the context, if we could hear Matthew's voice speak the words, we would understand by the inflection points alone.
Mathew was addressing the times Jesus' family was on the run from Herod. They couldn't stay in Bethlehem, so they ran to Egypt. He avoids the slaughter of the innocents. When it's all safe they can come back out of Egypt.
"But you, Bethlehem Ephrathah, though you are small among the clans of Judah, out of you will come for me one who will be ruler over Israel, whose origins are from of old, from ancient times." - Michah 5:2
"And out of Egypt I called My son. - Hosea 11;1
"A voice is heard in Ramah, mourning and great weeping, Rachel weeping for her children and refusing to be comforted, because they are no more." - Jeremiah 31:15
They said to him, “In Bethlehem of Judea; for this is what has been written by the prophet: ‘AND YOU, BETHLEHEM, LAND OF JUDAH, ARE BY NO MEANS LEAST AMONG THE LEADERS OF JUDAH; FOR OUT OF YOU SHALL COME FORTH A RULER WHO WILL SHEPHERD MY PEOPLE ISRAEL.’” - Matthew 2:5-6
So Joseph got up and took the Child and His mother while it was still night, and left for Egypt. He remained there until the death of Herod. This was to fulfill what had been spoken by the Lord through the prophet: "OUT OF EGYPT I CALLED MY SON." - Matthew 2:14-15
Then what had been spoken through Jeremiah the prophet was fulfilled: “A VOICE WAS HEARD IN RAMAH, WEEPING AND GREAT MOURNING, RACHEL WEEPING FOR HER CHILDREN; AND SHE REFUSED TO BE COMFORTED, BECAUSE THEY WERE NO MORE.” - Matthew 2:17-18
Mathew is not saying there's a specific verse, or prophet, that calls Jesus a "Nazarene", He is merely summarizing the events Jesus fulfilled prior to ending up where He did.
Therefore, NOW He shall be called a Nazarene. Matthew is simply stating a conclusion, the culmination of young Jesus' travels in His flight for saftey. Now He can find a place to rest his head, Now He will be called a Nazarene. This fulfils what the prophets said regarding Chris's young life on the run.
It probably could have been anywhere other that Bethlehem or Egypt.
Pick a town from the Old Time Jews:
If we shall be Kings and Priests, like Revelation 5 says, why not our own pope.
Peaceful Sabbath.
