Before I go into the details of the debate itself, it's important to point out that scientific models aren't good or bad because they're "true" or "untrue", but because of how well they can describe or predict things.

In order to falsify if human race exists, we need to define what race is. While it'd require a lower standard of evidence to compare to other biological use of the term "race", "breed", or "variety", I'm going to use subspecies as a means of comparison to race because it's the most well defined of the aforementioned taxonomical ranks.

Because most work on human subspecies is ethically charged, here's a definition used by biologists in regard to subspecies of wolves (source: https://www.ncbi.nlm.nih.gov/books/NBK542546/):

1. shared phenotypical/morphological attribute(s);

2. genetic compatibility with the species (i.e. two subspecies can mate with each other);

3. partial restriction of gene flow (i.e. just because they can doesn't mean they do);

Starting off with the phenotypical requirement, it's well established by physical anthropologists that it's possible to separate human skeletons into three or four morphological "ancestries" (Negroid, Caucasoid, Mongoloid, and possibly Australoid). Besides that we obviously have skin colour, hair colour, hair texture, face shape, etc.

Because no one genuinely thinks modern human races are different species, I'm going to skip #2.

Humans most certainly have partially restricted gene flow. Even in relatively diverse parts of the world like the United States, you have pretty high population heterogeneity in regards to race: https://www.vox.com/2018/3/5/17080218/school-segregation-getting-worse-data and a rate of interracial pairings substantially below what we would find by random pairing (lookup: OkCupid data, Tinder data, interracial marriage rates).

By the standards of how we define subspecies in other animals, we have subspecies in humans.