The relationship between you and this neuro is over and is not resurrectable. AND you will not change his mind with any number of statistics nor arguments.
I, too, feel that he is mostly coming from a position of concern, but is plying his argument with terror. It is hard, as a physician, to see someone reject what you feel is the only option. To put it in perspective, when I had a parent who refused all immunizations, I typically asked them to seek a new pediatrician.