They either taught you wrong or you misunderstood what they meant. Race is very much so a social construct. Human populations differ only on a gradient on the amount of DNA differences from different populations. The overlap is extreme. There is very little adaptive difference between human groups and we can all still interbreed.

Essentially, anyone who claims race exists genetically within the human race is trying to force a rectangle through a much too small circular hole. It doesn't work and it doesn't hold up. The consensus is extremely clear, race is a social construct.

The article you quote uses the term "traditional" and that's correct. These are the traditional definitions. But the traditional definition of race is superficial and not meaningful in showing genetic variation. It serves no purpose, and when you delve into it you'll pretty soon find that it is impossible to define race in a way which will hold up to even the most basic scrutiny. Even among animals and plants it's not really used anymore. It's too arbitrary and too subjective.