They don't. Among any race, there are a lot of genetic differences. The thing is that these differences tend to be pretty minor and superficial. As a species, humans have much less genetic diversity than a lot of other species - about 70,000 years ago, we went through a population bottleneck where only about 5,000 humans (give or take) survived. We're all descended from this surviving population, and diversity is decreased even further since most populations came from small groups that migrated out of Africa. We just haven't had enough time to accumulate significant differences, especially given that humans are amazing at migrating, and very few populations were truly isolated from one another.
Even on a purely genetic level, you have to remember that we're dealing with populations and their gene *pool*, not the genes of an individual. There's often more variation between individuals that we'd consider the same race than between individuals of different races. So while you can look at averages and general trends, they aren't usually applicable to the individual.
In other words, there's enough overlap in the "error bars" between different races that you can't draw a meaningful conclusion, or apply the statistics to an individual data point (i.e. a person). You can actually see this in medicine - there are some diseases that are more likely to show up in people of a given race, and some groups have genetic traits that make certain specific medications dangerous or ineffective. That said, knowing the patient's race doesn't determine the correct course of treatment for the individual - it just influences where to look first, and extra factors to take into account.
It doesn't make things easier that the concept of "race" is poorly-defined, and to some extent, arbitrary. There's a lot of overlap at the edges, and a lot of subdivision within races... and that's before you even take culture and social constructs into account. Long story short, it's not really accurate to say that race is purely a social construct, but it's also not a distinct thing - it's a way for us to categorize people based on a bunch of different social, geographic, and physical traits.
http://theness.com/neurologicablog/index.php/does-race-exist/