But I do not doubt that Jesus lived.
It is his claim of divinity that is extraordinary, and which requires more proof than the words of his followers.
My mother's claim to me, on the other hand, is not extraordinary. It is also very probable.
You reject the evidence, fine. Many did during Jesus's time and many did afterwords. Just realize that you are varying your standard of required evidence to suit preconceived notions of what is true. Even the Jews did not do this then. A man could not testify for himself but when 2 or more witnesses agreed, it was taken as truth.
My mother's claim to me, on the other hand, is not extraordinary. It is also very probable.
It is also probable she isn't your mother. Again, you have a sliding scale for what is required as evidence and this scale is based on preconceived notions of what is true. You believe your mother is your mother so you don't have much evidence to convince you. While you believe Christ wasn't divine so you require more evidence than what is humanly possible to provide.
There is nothing wrong with a sliding scale, its just important to understand how your own bias affects your thinking and your acceptance of what is true.