“Race” is more of a social construct than a biological distinction. That doesn’t mean “races” don’t exist, it just means it’s difficult, if not impossible, to label people with a distinct, finite number of races.
To help understand why it is so difficult to biologically distinguish races, look at the difficulty biologists have with distinguishing species.
One way you can define species is if the males and females can produce offspring. Well, a horse and a donkey can produce offspring, as can a lion and a tiger, but neither of these are the same specie.
One thing to note about the possible hybrids above is that neither is fertile - they can’t reproduce on their own. So we could further our definition of species to be if the males and females can produce fertile offspring (in fact, this is the definition that Wikipedia uses). But there’s another problem with that.
Say you have three groups of animals: group A, group B, and group C. Group A can produce fertile offspring with group B, and group B can produce fertile offspring with group C. Group A, however, cannot produce fertile offspring with group C. How should we distinguish these groups - three species? one?
There exists some birds that represent the situation in the last paragraph, so it isn’t uncommon. This situation where only certain groups can reproduce is known as a ring species.
With the difficulty distinguishing sexual species, imagine the difficulty involved distinguishing asexual species.
What does this all have to do with race being a social construct? If it is difficult to consistently discriminate what a specie is, how much more difficult would it be to distinguish races? The problem with race is more that they are completely arbitrary and who belongs to what race has changed several times since the term was coined.