I think you're making a good point overall. If a trait is heritable then it will vary by populations. People should understand the consequences of the position they're arguing.
However, why do you believe that IQ is not heritable? It's hard to believe there is no genetic component that is heritable. Humans evolved over time from other species, and in the process of evolving into Homo sapiens sapiens, their intelligence was inherited and selected for strongly. There's nowhere else for the foundation of human intelligence to come from in the first place other than inherited genetic traits.
As a peer comment asked, "If IQ is not heritable, then how did it evolve?"
I suppose it's possible that a large component of intelligence could come from society and nuturing. Humans have gotten more intelligent as their diet has improved, and as their diet has become more stimulating, and with writing and education. Still, the fundamental capacity to have a verbal or written culture, and to teach and learn, arises from our baseline intelligence which is possible due to our genetics.
To be fair, you might believe that all living humans have indistinguishably similar IQ at birth. There are reasons to believe it's not true, but it's a consistent belief. However, it would not be sensible to believe that IQ is stable over time, since we know that humans evolved IQ that was not previously present in proto-humans and ancestral species. Therefore IQ must be subject to genetics, and therefore must be partially heritable. From this position you might believe that IQ is heritable but does not genetically vary to a meaningful degree in modern populations. This position makes sense.
However, by comparison, it would be fairly incredible to believe that IQ is not heritable whatsoever, especially given that intelligence is affected by physical traits such as size of skull and brain, and by metabolic pathways and disease and disease resistance. Brain size for example is correlated with intelligence [1]. A number of diseases are known to affect intelligence, such as phenylketonuria. I understand in your comment you acknowledged that such diseases might impair someone and drag their intelligence down -- but just as different people have different potential as athletes, as measured by their VO2max, why wouldn't you believe that the physical systems underlying intelligence couldn't be just a little bit different in one population versus another, thus resulting in a little bit of an edge in IQ? Humans are so different in height, weight, muscle, skin/hair/eye pigment, that it would be incredible if we all were exactly, immeasurably different on some treat that also distinguishes humans from other species.
Science has explored this topic, and my understanding is that modern research on this topic suggests that IQ is heritable. Studies examine factors like twins who were separated at birth, and grew up in different households. Could you share the reasons why you think it is not?
> Various studies have found the heritability of IQ to be between 0.7 and 0.8 in adults and 0.45 in childhood in the United States. A 1994 article in Behavior Genetics based on a study of Swedish monozygotic and dizygotic twins found the heritability of the sample to be as high as 0.80 in general cognitive ability; however, it also varies by trait, with 0.60 for verbal tests, 0.50 for spatial and speed-of-processing tests, and 0.40 for memory tests. In contrast, studies of other populations estimate an average heritability of 0.50 for general cognitive ability.
https://en.wikipedia.org/wiki/Heritability_of_IQ#Estimates_o...
[1] "Overall, larger brain size and volume is associated with better cognitive functioning and higher intelligence. The correlations range from 0.0 to as high as 0.6, and are predominantly positive." https://en.wikipedia.org/wiki/Neuroscience_and_intelligence#...