Some argue that since the prophecy in Matthew 2:22-23 about Jesus being a Nazarene is not found explicitly in the Old Testament, it demonstrates that there is a mistake in the Bible. However, there are several reasonable explanations that would resolve this alleged problem in the Bible.
22 But when he heard that Archelaus was reigning over Judea in place of his father Herod, he was afraid to go there, and being warned in a dream he withdrew to the district of Galilee. 23 And he went and lived in a city called Nazareth, so that what was spoken by the prophets might be fulfilled, that he would be called a Nazarene.
Matthew 2:22-23
There are at least two possible explanations for believing that Matthew 2:22-23 is not a mistake in the Bible:
The Hebrew word for “branch” in Isaiah 11:1 is ‘netser”, and since Hebrew was written with only consonants, this word would have appeared as NZR, which are the same consonants found in Nazarene.
So, it is possible that Matthew is using the word “Nazarene” as a kind of wordplay to refer to the “branch” in Isaiah 11:1.
In the first century, Nazareth was a small town with a negative reputation. In [https://www.biblegateway.com/passage/?search=jn+1%3A46&version=ESV John 1:46], Nathanael says, “Can anything good come out of Nazareth?”
It is possible that Matthew is using the word “Nazarene” to refer to someone who is despised, or looked down upon. If this is the case, then these prophecies from the Old Testament may be relevant:
6 But I am a worm and not a man, scorned by mankind and despised by the people. 7 All who see me mock me; they make mouths at me; they wag their heads;
Psalm 22:6-7
He was despised and rejected by men, a man of sorrows and acquainted with grief; and as one from whom men hide their faces he was despised, and we esteemed him not.
Isaiah 53:3
To read more answers to alleged and apparent contradictions in the Bible, see “Contradictions” in the Bible Answered.
These books are also excellent resources:
Evidence That Demands a Verdict: Life-Changing Truth for a Skeptical World - Josh and Sean McDowell
Little Pilgrim's Progress (Illustrated Edition) - Helen L. Taylor