I also don’t see any substantive theory behind the claims, other than that it seems very intuitive to people that (1) the sex of a baby should be predictable and (2) sex ratios should vary a lot.

I think the basis for that first intuition is gender essentialism: men and women are so clearly different that it just stands to reason that they should somehow be externally distinguishable (in the pre-ultrasound era) even in the womb, and that the sex of the baby should be influenced by various ways as might be explained by gender essentialism.

I think the basis for the second intuition is what Tversky and Kahneman called “the law of small numbers”: everybody knows someone with several siblings, all of the same sex. People don’t have a sense of the huge sample size that would be needed to learn anything useful from such data, even setting aside selection and recall issues. Also, gender essentialism: it just stands to reason that parents of boys should be more masculine, in some way, than parents of girls. This bit of intuition can be backed up by endless speculation of the sort that is called evolutionary psychology and which plays well in Freakonomicsland.