Suggest that you take the time to research the area yourself, rather than me point you in a given direction.
The statement "the brother of Jesus, who was called Christ, whose name was James" was the obscured statement I was referencing in my original response. It is agreed by a majority of scholars that this statement is authentic. My reference: Louis Feldman American Professor of classic literature .
Jesus Outside the New Testament: An Introduction to the Ancient Evidence by Robert E. Van Voorst pg 88
Josephus: The Essential Works by Flavius Josephus and Paul L. Maier 1995 pg 285
I personally don't know if Jesus exist, nor does anyone alive. However, your question was related to why people believe in him. I answered because of fear of death, and since there are some references to him by Josephus.
This thread wasn't originally an argument for the support or denial of the existent of Jesus, nor do I make an attempt at such a statement. I'm only stating why people believe in him, and now that not all believe the references in Josephus are not authentic as stated by you.