Yes, race is a social construct. I am a living, breathing example. I have very pale skin, blue eyes, and fine, straight hair. Everyone would call me white. However, my mother has olive skin and wiry hair -- and comes with a family bible which depicts interracial relationships (which yielded our descendants) back in the slave days. My father, who comes from a Native American background, has pink skin and green eyes ... and his heredity, although it is not in a bible, is descendant from the Blackfoot tribe. A cousin still lives in the region. All this, and the skin and eye colors, means my family is as mixed race as they come.
But what does it mean? I look white. Folks call me white. They say I belong to the white culture. I know differently, but the skin tone and eyes don't lie, do they? There is so little melanin in my skin. (When I say pale, it means I don't tan.) Well, it does lie. Using such superficial characteristics doesn't help ... it's the blood, right?
But didn't the mapping of the DNA code of man prove that race is not a genetic marker? Didn't they say there is no difference between races besides where genetic mutations formed and became dominant?
I think people first determined race to be an easy out, an easy way to tell where a person's descendants came from. And that used to be so easy. All the folks from Africa had excessive melanin to protect their skin from skin cancer. So you saw a dark-skinned individual and knew they were from Africa. With our ease of transportation these days, and the mixing of the cultures and "races", you simply don't know anymore.
It has a lot to do with people wanting to be superior too. In my family, the olive skin is prized. In families and cultures we have unusual ideas about what is better -- for instance, look at the present celebrity prizing of super-skinny. It's an unusual thing to cherish and we all know it will be gone soon. So where does that leave us with this topic? Race is a social construct. It may have begun originally as a comment on skin tone, hair texture, eye color, and eyelid fold, but it has transpired into an ugly superiority issue, which we know is not true. As the world "browns" through interracial, interethnic progeny, I think we will see a transformation of the ideals. Of course, that will likely be in another 1-2 K years. :)