When an individual describes someone who is related to him or her biologically as "not really kin," what is he or she saying?

Kin can be described as a term which is often used for family or relatives.

When a person says 'not really kin' for his biological member of the family he means that although the person is a a part of his family but he might have taken certain actions to hurt the other family members. The person is a part of the family but due to his actions he/she is not considered to be the part of the family.  The relative has not exercised her rights or fulfilled her obligations as a family member.

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