Actually, this is a message that is found in many world religions if you examine closely, it is rather short sighted to focus on the biblical examples. Of course, I doubt it's to be taken literally. Simply put, interpersonal relationships are dependent upon the individuals involved, if an individual goes through some kind of dramatic change then any relationship with that individual automatically changes, whether it be familial ties or anything else.
This could be applied to the JW shunning policy: A member of the family becomes enlightened regarding the religion and chooses not to follow it anymore, but if the rest of the family regards him as apostate then there will certainly be disharmony.