[cactusface]

Different races cannot interbreed, but only because they are geographically isolated.

Different species cannot interbreed (generally speaking), even if they are not geographically isolated.

Humans are not geographically isolated. Geographical barriers have contributed to the creation of population groups, but these are distinct from races in that there is a mechanism for DNA to move between them (somebody takes a trip and makes a baby).

Anyway, Wikipedia says in the lead sentence of that article I linked to that simply classifying people into discrete races is scientific racism.

"Scientific racism is the use of scientific techniques and hypotheses to support or justify the belief in racism, racial inferiority, or racial superiority, or alternatively the practice of classifying individuals of different phenotypes into discrete races."

[theorique]

"Scientific racism is the use of scientific techniques and hypotheses to support or justify the belief in racism, racial inferiority, or racial superiority, or alternatively the practice of classifying individuals of different phenotypes into discrete races."

The first three actions refer to value judgments ("better" / "worse" - compared to what? for what purpose?). Most people would agree that science should steer away from such judgments.

On the other hand, "classifying individuals of different phenotypes into discrete races" seems distinctly unproblematic. There are different clusters of genetic types that arose due to relative geographic isolation, and gave rise to various differences and adaptions. Obvious examples of these include skin color, hair color and texture, average height and build, and so forth. I did not realize that making this observation, in the absence of value judgments, was now interpreted as "scientific racism".

[cactusface]

The problem is only that there are not discrete categories. For starters, how do you classify children of parents belonging to two discrete racial groups? And their children? And so on and so forth. Well, people have been spreading their genes around the globe for a long time, and the upshot is we all belong to the same racial group. Sure, there are clusters, but there are not purebreeds.

Further, culture / ethnicity is just a much more accurate way to classify people than genotype or phenotype. I don't have a source for this, but I believe the best way anthropologists have come up with to group people is by the kind of food they eat.