That's a lod of BS.! I have both Allergies/Asthma and 2 Yorkies, a full grown one and a puppy. Their hair has nothing to do with my Respitory problems!
It's a well known/published fact!!!
He is just fishing for another way to hurt your Family and the situation, pets get caught up in Divorces too, in a round about way? As well as children.
It's always a bitter/sticky situation.