Standard archaelogy: "It doesn't exist unless I have physical evidence." This one is pretty silly, actually. This position is an academic oddity because it is pretty much always proven wrong.
Also the term Nazarene didn't mean someone from Nazareth, but a member of a sect.
Are you thinking of Nazirite? As in Samson? Judges 13:4-5
Now see to it that you drink no wine or other fermented drink and that you do not eat anything unclean, because you will conceive and give birth to a son. No razor may be used on his head, because the boy is to be a Nazirite, set apart to God from birth, and he will begin the deliverance of Israel from the hands of the Philistines."
Well, I don't know. The Gospels were written within the lifetimes of people who were there, and they mention Nazareth -- are you suggesting that they simply made up the name?