Heritability and heredity are not the same thing.
Heritability is the tendency for populations to display similar traits as their ancestors over time due to genetics.
Heredity is the passage of genes to offspring, and the traits resulting from that.
A lot of traits are heritable, but also influenced by environmental, cultural, historical, and social reasons that lead to their being huge outliers. Heritability is a trend, not a rule. It has to do with populations, not individuals.
There is not a lot of strong evidence that intelligence is any more highly genetically heritable than obesity or susceptibility to certain environmental cancers; you can be born with the genetic predispositions, passed down from your parents, but they will only get you about half of the way there.
Edit: changed wording and provided other examples.
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