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The fact that he claims so authoritatively and certainly that there is zero effect which is hubris manifest. it is also incorrect for the arguments I have or at best rather incomplete.
The null hypothesis is always false, and effect sizes are never zero. When he says it's zero you should probably interpret zero as "too small to care about" or "much smaller than most people think". I'll bet the studies didn't say the effect was literally zero, they just said that the effect isn't statistically significant, which is really just saying the effect and the sample size were too small to pass their threshold.
People say a lot of things that aren't literally true, because adding qualifiers everywhere gets annoying. Of course if he doesn't realize that there are implicit qualifiers, then he's mistaken.