Because the father is supposed to be the head of his house. If he cannot preside over his own house in "fine manner" then they suppose he cannot preside over the congregation very well. He and his family are supposed to be an example to the congregation.
I agree with that. I have heard that argument, too. My dad was made to step back as elder right after I didn't show up with my parents at the KH anymore (my parents made me show up until I was 16 although I already told them aged 13 that I wouldn't be a JW). He had to step back although I was never df'ed oder da'ed officially as I never got baptised. He became elder again after about 4 or 5 years. He felt very bad about losing that position but he accepted it as punishment as he was not able to win me back i.e. do a good job as head of his house. That's what he himself told me. He failed so he had to be punished. Off course he felt he owed it to Jehovah to be punished, not the WT.