Culture and family
Besides being a way to ensure that only Indians got the pitiful and paltry benefits that the federal government was giving to the Natives they made treaties with, blood quantum was an insidious way of permanently removing the land and memory of a people (HCN, 1/19/09).
What has happened to many Native families is a tragedy. To be told you are no longer native because you fail a minimum blood quantum must be heartbreaking, and it's totally false. Many Eurasian peoples moved and interbred over centuries of war, conquest, migration and political alliance. They were who they were by culture, ethnicity and nationality. It was kinship, family and self-declaration that made them Hungarian (East Europeans mixed with Mongol), Spanish (Celts, Iberians mixed with African and Arabian) or Italian (Mediterranean diaspora).
Many tribes have rid themselves of the blood quantum system while others have reinstituted it because of casino greed. No matter how you look at it, blood quantum is about exclusion when times are good and inclusion when times are bad. If money and benefits abound, the rolls are restricted so it can't be shared.
Blood quantum is especially cogent to my situation. I am Mexican (part indigenous/part European) and although I look completely Native, I have to prove my heritage. Natives are Natives by culture and family, not solely by blood. If you don't believe me, try looking into the eyes of your blond-haired niece and telling her she is not part of you and your heritage.