If races exist, then one must be supreme.

Much of the Race Does Not Exist cant stems from the following logic (if you can call it logic): “If there really are different racial groups, then one must be The Master Race, which means — oh my God – that Hitler Was Right! Therefore, we must promote whatever ideas most confuse the public about race. Otherwise, they will learn the horrible truth and they'll all vote Nazi.“

Look, this is one big non-sequitur: Of course, there are different racial groups. And of course their members tend to inherit certain different genes, on average, than the members of other racial groups. And that means racial groups will differ, on average, in various innate capabilities. But that also means that no group can be supreme at all jobs. To be excellent at one skill frequently implies being worse at something else. So, there can't be a Master Race.

Sports fans can cite countless examples. Men of West African descent monopolize the Olympic 100m dash, but their explosive musculature, which is so helpful in sprinting, weighs them down in distance running, where they are also-rans.

Similarly, there are far more Samoans in the National Football League than Chinese, simply because Samoans tend to be much, much bigger. But precisely because Samoans are so huge, they'll never do as well as the Chinese in gymnastics.

Every person falls into a single clear-cut racial group.

This one is so silly that I doubt that anybody who has thought about race in the real world for more than ten minutes believes this. Nobody can agree on how many racial groups there are, exactly who is in each one, or what to call them.

Since nobody can agree on how many racial groups there are, exactly who is in each one, or what to call them, then race does not exist. 

This one's equally daft. Outside of mathematics, and of human inventions like the law, categories almost always fall across continuous dimensions. Where does “young” end and “old” begin? It all depends on the situation. For example, among female gymnasts, 18 is “old.” Among architects, 45 is “young.” Yet that does not mean that “age” is meaningless. Further, categories are typically fuzzy. Few people are 100% “sick” or 100% “well.” But “health” is still a useful concept.

The best example of the fuzziness of natural categories is the concept of “extended family.” All the criticisms made about the fuzziness of racial groups apply in spades to extended families. How many extended families do you belong to? Well, at least two: your mom's and your dad's. But they each belonged to their parents' two extended families, so maybe you belong to four. And your grandparents each belonged to two …

And what are the boundaries of your various extended families? If the question at hand is who you'd give a spare kidney to, you'd probably draw the limits rather narrowly. But, when making up your Christmas card list, you probably toss in the occasional third cousin, twice removed. And exactly what's the appropriate name for all these extended families anyway?

In fact, extended families are even less clear-cut than racial groups. Yet, nobody goes around smugly claiming that extended families don't exist.

But why is extended family such a perfect analogy for race? Because it's not an analogy. They are the same thing: kin, individuals united by common descent.

There's no natural law defining where extended families end. A racial group is merely an extended family (often an extremely extended family) that inbreeds to some extent. It's this tendency to marry within the group that makes racial groups somewhat more coherent, cohesive, and longer lasting than smaller-scale extended families.