Why is the mechanism of inheritance for this disease autosomal dominant?
I think this question is not possible to answer without knowing the frequency of the deleterious alleles in the population.  There's no way to assess whether incomplete penetrance is more or less likely than an undetected mutation in the mother's side.  Since the question doesn't mention the mother's family at all, and only the father's, that suggests to me that the question writers don't want you to think that anything is wrong in the mother's side.  That would make it dominant with incomplete penetrance.