You misunderstand. Perhaps "doesn't exist" isn't the right term, that was wording on my part. What I mean is our social concept of race is inaccurate, it tends to change quite often and varies culture to culture. Scientifically race doesn't exist, only our apparent traits do. For instance, there's actually much more genetic diversity in Africans than any other race, both in genes and in appearance.(Even in skin tone.) Yet, now they're mostly regarded as one race.
Yet many races we refer/referred to as different are much more similar. For instance, even though jews are refereed to as a different race by many, genetically they're pretty much Caucasian in the same sense that we refer to as all africans as just africans, the same goes for the Irish.(Who were considered a different race for quite awhile, but are now considered white.)
The point being that it isn't as clear cut and defined as culture makes it out to be. And it isn't nearly as drastic as something as a pug or a beagle, false equivalence there. Outside of skin tone and facial characteristics(which also vary even within one race) we are very similar to each other. Especially compared to non-homo sapien humans that are now extinct.(Such as homo erectus, though certain people cary a bit of their genects due to homo sapeins breeding with them.) That would be more so like the difference of a beagle and a pug. Aside from appearance(which most humans are drastically different from one another anyway even within the same race when compared to other species), there's hardly a difference between everyone of us at all. It's nurture that makes us so different otherwise, not nature. A racist believes, however, that nature is why certain 'races' behave differently and that they inherently possess those characteristics.