I'd work at him from the angle that it is possible to be both professional and personable. If you pull out editorial from a high quality newspaper or even cite some influential blogs in a space he follows you should be able to put that point to him pretty convincingly.
Alternatively I think Will Critchlow recommends hiring people on Amazon Turk to answer a Panda-style questionnaire. You could compare the current text with that written in the first person and see which one real people prefer. Or pitch the two versions of the text head to head in an A/B test and see which has higher user engagement statistics.
If you're only doing the blog to generate links/shares etc. and he insists on using his own writing style then it sounds like it would just be a waste of his time.