How did they control for maternal IQ if they used questionaires? Did people self-report their IQ? What about paternal IQ?

What was their response rate?

A recent study in English showed the entire variation in IQ between breastfeeding and non-breastfeeding children was explained by parental IQ. The average IQ of the parents of breastfed children was 15 points higher (an entire standard deviation). Probably because breastfeeding is an ideological quirk of the educated.

And, of course, this study assumes IQ actually measures something. Which most evidence suggests it doesn't.