Except that no one in ordinary discourse uses "race" in the way you are, which means "species" (the whole not-interbreeding thing is often taken as definitive of "species".)
"Race" as it is commonly used means "variety" or "breed", and the claim that there are observable and significant statistical differences between human populations in geographic regions is, one hopes, uncontroversial. Those differences come from different genes, and since we all know that a trivial edit to a single gene can result in a massive change in function, it is reasonable to ask about a wide range of characteristics that have some genetic influence.
To claim that "races" in this sense "do not exist" is to come across as incoherent and pedantic at the same time.
Whenever anyone has looked at any characteristic that is really significant in society and how it differs across "races" so defined, they have found that the differences are trivial at best, non-existent at worst. This is "controversial" because a bunch of idiots want to project their prejudices onto genes.
"Intelligence" is by far the most debatable target for this kind of nonsense because a) it is controversial as to whether or not anything like "g" is an objectively real feature of human beings; b) it is extremely controversial how heritable it is; and c) even if it is real and heritable, our ability to measure it is so poor that it is very difficult to make any claims about population statistics.
See... you can actually refute racist nonsense while at the same time acknowledging what everyone knows: varieties of humans exist, and redefining the word "race" so it does not apply to those varieties of humans does not make the fact that varieties of humans exist go away.