An intellectual miasma exists within public discussion of racial equality. Most people readily accept differences between individuals. Most will even accept that genetics plays some kind of part in said individual differences, but all differences suddenly become environmentally causes when cognitive abilities in racial groups are judged. Not only is this wrong, but these people essentially have blind faith in what appear to be miracles.
1. Prima facie necessity
Different groups would have had different environments to contend with. For example, some places may have had malaria prominent, and so developed immunity to it became necessary. Some animals may have needed group coordination to kill, and hence social ability was now selected for. Harsh Winters required pre-planning and delayed gratification (saving food), and so those who had the ability to develop these traits were selected for. Clearly, prima facie, there is need for certain cognitive abilities.
Also add culture to the mix, and evolution speeds up by a factor of 100. Moreover, in the last 5,000 years, the advent of civilisation started selecting for people who were capable of being civilised (in various ways) (https://www.pnas.org/content/104/52/20753.abstract). For example, England's "war on murder", a time in English history wherein criminals, of all kinds, were sentenced to death for their crimes, had a significant eugenic effect on criminality (https://journals.sagepub.com/doi/full/10.1177/147470491501300114). If all races were equally criminal, then England selectively killing off criminals would mean that those countries not doing that would have more people with criminal tendencies.
But we also have physical differences which demonstrates that differences do exist...
2. Physical differences
We have more than a century worth of research which shows that the races differ in brain size. Sean Last (2016) created a comprehensive article detailing these differences and why they exist (hint: it's partially genetic). In short, the arguments for their existence, and the fact that they are at least partially genetic, is as follows: "the differences are present at birth, around the world, the Black/White brain size gap is not smaller today than it was 100 years ago, mixed race individuals have brain sizes in-between their parent’s races, and, finally, traits that typically co-evolve with brain size differ racially in a way that mirrors brain size differences." (https://thealternativehypothesis.org/index.php/2016/04/15/brain-size-race-and-iq/).
It is also possible to predict someone's race by looking at the shape of their brain, because the human brain contains "rich ancestral information" (https://www.cell.com/current-biology/fulltext/S0960-9822(15)00671-5).
In fact, it's the brain wherein the most pronounced genetic differences between races can be found. In other words, if we were looking genetic racial differences, it's best to start in the brain because that's where a lot of the difference is found https://bmcevolbiol.biomedcentral.com/articles/10.1186/1471-2148-11-16
The physical differences contradict the conception of cognitive racial equality.
3. Neanderthal admixture
Once humans left Africa, they met and bred with other species or subspecies of humans. These other humans had been evolving independently from us for a seriously long time, and they are universally accepted to have been different from us physically and mentally, as a result of evolution (https://www.nationalgeographic.com/science/phenomena/2013/03/13/from-neanderthal-skull-to-neanderthal-brain/). Some populations bred with these groups more than others (https://www.researchgate.net/publication/259984758_Resurrecting_Surviving_Neandertal_Lineages_from_Modern_Human_Genomes). Africans didn't breed with them at all (https://news.harvard.edu/gazette/story/2014/01/neanderthals-dna-legacy-linked-to-modern-ailments/). Hence, there is differing degrees of Neanderthal admixture in different races of people.
So, for example, mental traits such as nicotine addiction and depression were found to be related to Neaderthal DNA (https://www.theguardian.com/science/2016/feb/11/neanderthal-dna-may-account-for-nicotine-addiction-and-depression).
So, how is it possible for the races to be cognitively equal, when their levels of Neaderthal DNA differ, and Neanderthal DNA is known to result in different mental traits?