Exactly, we agree, a teacher. Just a nameless guy of some description,
Why not an actual man called Jesus?
was he born in Bethlehem?
No of course not. That was invented to connect him to an OT prophecy. Matthew and Luke use very different stories to achieve that.
Did he claim to be the messiah and have 12 apostles?
I think he did make claims of that sort. Otherwise an account that was entirely fictional would not include failed claims.
Jesus's existence is crucial to the narrative, Socrates's existence isn't
Why? Are the words attributed to Socrates any less interesting if they were written by somebody else and put in the mouth of a mythical Greek philosopher?