If you don't believe in race, there is something seriously wrong with your epistemology.
When people say "race isn't real", they prove too much. This argument is strictly correct, but it applies to all concepts. Concepts aren't "real", they are useful, they are mental tools. "Chairs" are no more "real" than "races", but "chair" is a useful construct. The only measure of the worth of a concept is how useful it is, not whether it is "real" or not. All words are social constructs, because words do not have objective definitions; their definitions are agreed socially. That does not mean words are not useful! I do not say words including "race" refer to real objects. Instead I say they are useful (or not useful).
Is "race" a useful concept? Yes, because it allows people to make accurate predictions. If I say someone is black, you can predict their ancestry is mostly from Sub-Saharan Africa. If I say someone is from the Sub-Saharan race, you can predict their appearance, and their likely susceptibility to sickle cell anaemia.
But how do we classify people into races? Where does one race stop and another one start? What about people of mixed race? The "racial purity" argument is sometimes used to denigrate the concept of race. The argument goes: even if a person can be half one race and half another, that implies that "pure" races exist. Either each parent was a "pure" member of one race, or had ancestors who were. All branches up one's family tree will eventually hit a pure ancestor, a member of a single race. Since this is not true, because the races have not existed forever because humans have not existed forever, and probably everyone has a tiny bit of DNA from all races anyway, thus, the argument goes, races do not exist.
This argument is misguided, because it sets up a foolish requirement for the concept of race, which it then knocks down. But "race" doesn't have to be pure to be a useful concept. "Species" is a useful concept, even though species hybrids are common in plants, and ring species exist. "Purity" supposes races have existed forever, sprung into existence is pure form, later to be intermingled. But of course they haven't, humanity hasn't existed forever. Races don't have to have existed forever for the concept to be useful. If you take a random sample of people from around the world, and genetically isolate them, after several generations that population will have become genetically homogenous. Hey presto, you have created a new race. That is pretty much how Ashkenazi Jews came about. To prevent races diverging, you need gene flow/immigration of about 2% of the population per generation. The actual figure. "The average number of migrants per generation between sub-Saharan Africa and Europe, over the past hundred thousand years or so, was 1.26." 1.26 individuals is far below 2% of the population.
It is not true that everyone has a little bit of DNA from every race. Given that you have far fewer slots in your genome than you have ancestors, you have plenty of ancestors from which you have not inherited any DNA. Even if one of your distant ancestors was from a different race, you are unlikely to have any DNA from that race. (Selection pressures will change this probability one way or the other.)
You have many more slots in your family tree than people have ever existed. If you go back 40 generations, you have a trillion slots in your family tree. But 1000 years ago, there were not a trillion people on Earth. Many slots are occupied by the same individual, and some individuals occupy many more slots than other individuals. A typical Englishman today is much more closely related to people living in England 1000 years ago than to people living in Sub-Saharan Africa 1000 years ago (or today).
The fact that ring species exist knocks down the complaint about the fuzziness of the races. Even though "species" or "race" are fuzzy concepts, they are still useful. People in North Africa have more Sub-Saharan DNA than people in Europe. A concept of race that could not deal with this, that required "purity", would not make accurate predictions. But a sensible concept of race has no problem with fuzzy borders. It simply says that genetic gradients will be greater in some areas than others. A physical border like the Sahara has produced a steeper genetic gradient between North Africa and Sub-Saharan Africa, than within Sub-Saharan Africa itself, where there is more gene flow and more homogeneity. It doesn't mean interbreeding is impossible, any more than interbreeding between species is impossible (though less common, less probable, with lower chance of success).
How many races are there? Are there subraces? This question is misguided. How many families are there? Are you a member of one family or several? Families can overlap, and a race is just "an extremely extended family", one that is "partly inbred", as Steve Sailer put it. Race is a useful concept, even though you are not able to say how many there are, or whether a group of people counts as one race or two. "Family" is a useful concept as well, despite having the same "shortcoming".
However, scientists do have a concept called a fixation index, of the genetic distance between two people. For a given arbitrary cutoff value, it will tell you whether two people are in the same race or not. So the number of races depends on the cutoff value you choose. This is not particularly relevant to making useful predictions, but it is somewhat relevant! For example, the fixation index between coyotes and wolves is 0.153. The fixation index between Europeans and Sub-Saharan Africans is 0.153. Sub-Saharan Africans are about as different from Europeans as wolves are from coyotes.
How do you tell what race someone is in? Clearly, when we talk about race, we are talking about ancestry. You can't just use appearance, because of convergent evolution. It is possible that two branches of humanity can end up with similar features. For example, Tibetans and Andeans are both adapted to high altitude, but they are not the same race. (The adaptations are different, with different genes.)
If I say someone is Sub-Saharan, or black, I mean they are descended from a population that lived there for a long time, with very little gene flow from other areas. Someone who has just moved to Africa does not become part of that race.
Isn't this circular? You are a member of a race because you are descended from people who lived there a long time; people who lived there a long time are the Sub-Saharan race. It doesn't matter if this is circular, because that is how concepts are bootstrapped. If I know your ancestry, I can predict your traits; if I know your traits, I can predict your ancestry. If I know your traits, I can predict your other traits.
Darwin called his book "the origin of species". What were the origin of species? Races! A population splits into two, with so little gene flow between them that they start to diverge genetically. After a time, they will be so different that we call them races. But they are still the same species -- they can still interbreed. The process could still be reversed: the populations could be brought back together, gene flow increased, and they would become one race again. But if the genetic isolation persists, after more time, they will diverge so much that interbreeding becomes very unlikely (though ligers and tigons are fertile). Now they are two species. With more time, they will diverge genetically still more, and interbreeding becomes totally impossible. They will forever be separate species.
Races are the origin of species. If races didn't exist, species could not exist. Species do exist, therefore races exist.