I think perhaps going down the allergy-ridden/medical issues path might be a good spin on things too, as although my parents don't know this (I think anyway) there are lots of allergies/medical issues on DH's side (e.g. lactose intolerant, wheat allergies, nut allergies, coeliac disease, epilepsy (don't think my parents realise DH has this in fact!))
Blaming it on DH's genes will be less likely to offend your Dad. Throw in that DH was susceptible to cold and chest things as a child and had numerous infections. That's probably why my MIL didn't mind so much, we blamed me and my side of the family.