People with a white parent and a non-white parent always claim the race of non-white parent. Why?

Society seems to indicate that is the rule. If the genetic ratio is considered to be 50/50, why is the white half ignored? Could it be the perpetual adherence to the white supremacist concept of racial purity - intentional or not?

There is a classification as bi-racial or mixed. Why do these people get the privileged convenience of changing between this and the non-white racial group?