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Of course it is heritable. The uncomfortable question is if its genetic.

With the monozygotic twin correlation being twice the dizygotic twin correlation, what other explanations are there?

Is been fairly well established empirically that monozygotic twins are treated differently than dizygiyic twins. Specifically, they share a much more similar environment than dizgoyic twins.

In other words, the equal environment assumption does not hold in reality.

How do you prove that? Environment are in large parts shaped by your genes. If you are an easy to please baby then your parents will like you more. If you sit quietly and study in class your teacher will like you more. If you are good looking people will want to be your friend. Basically the environment adapts to your natural traits and makes them stronger. This variance gets attributed to your genes and not nurture, since the environment was shaped by genes and not by artificial means like parental intervention.

Even if we accept this argument (I don't, to be clear), it could well be that what's heritable is the way MZ twins are treated versus the way DZ twins are treated, not self-control.

In that case, the fact that twin studies conclude that self-control is heritable is an artifact of the twin method.

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