"Races do not exist" ...

or "are social constructs"

What the fuck does that even mean? It is pretty obvious that they do. I seriously do not get it. Does anyone here have the knowledge to defend these seemingly ridiculous statements from a scientific perspective?

The correct statement is that there is no scientifically rigorous definition of "race".
For instance, there is greater genetic variability among groups indigenous to Africa than there are between some "white" people and one of those groups.
Distinctions along phenotypical lines are generally going to be pretty arbitrary.

Prejudice as prior probability isn't too useful as there aren't enough statistically sound correlations between (already established as poorly defined) "race" and behavior. (Though a lot of credulous people with poor critical thinking skills have been lead to believe there is.)