Firstly, it's not a universal thing. Race is a social construct, who is considered "white" or "black", or a member of any other racial group, changes depending on where you are in the world, and the culture and history of that society and country. In South Africa for instance, mixed race people are considered, and self identify, as their own ethnic cultural group, known as the coloureds (not a racial slur in South Africa). Many things affect this, from apartheid racial classifications from the past, to cultural differences from being raised in a certain home environment. In other parts of sub Saharan Africa, people who would be considered black in the USA and/or the West, are considered mixed race or even white.

As for why that's the case in the US, one just has to read up on the "one drop" rule in the United States, and it's ramifications on modern day understanding of race in US culture and society.