Regarding: "...why is the child of a so-called white person and a so-called black person so very often called a black person? "
- Good question. Probably reflects old laws for separation of the races in the USA -- if you have any black heritage you were black regardless of how you appeared, and then the co-option of the effect of those laws by the black community so that even if you could 'pass' you were still black. 
- In a way President Obama experienced this himself. His heritage is Kenyan & Irish American, however many people saw and spoke about him as African American. President Obama experience of racial prejudice premised on the colour of his skin is part of the source of his compassion and empathy.