Let me tell you something that took me years to figure out. Your father picks up on your stutter because he has the confidence issues himself. He feels like your stutter somehow defines him as a man or as a father. And in my honest opinion he might be a major influence on that judging by the way he reacts to it. Why do I think that way? I spent the last year in therapy working out through issues with my mother. Does your father show any narcissistic traits? Cause this sounds like one of them.