His son is an embarrassment to the family, he is the father of an illegitimate son conceived during an adulterous affair.
Worse, he refuses to pay child support or to have anything to do with the child and his mother (he has a restraining order preventing the child & mom from contacting him). He almost certainly pushed the mom to have an abortion (thusly - it is rumored - causing a serious rift with his father) the mother/mistress choose to have the baby anyway and Chris Buckley behaves as if the child doesn't exist.
WFB2 was a gentleman and class-act in every way... his son is something else entirely.