I read this a while ago so I may have forgotten details and my memory of cell biology and genetics might be rusty. They are saying X chromosomes carry intelligence. Females are XX. Males XY.
Assuming a situation in which the X chromosome carries intelligence and that intelligence is dominant:
A female child would have two X chromosomes. One from mom, one from dad. If dad is “intelligent”, and if it is mainly the X chromosome that carries such intelligence, then a child who is female can inherit the smart genes from dad regardless of the mother’s X genes. The mother could be average, with average Xs, and her daughter would still be smart because of her dad (who inherited a smart X from his mom). Bonus if both mom and dad are smart and each passes on smart X. Either way, you know dad is smart. You know he is passing on a smart X. Therefore his female children should be smart.
However, if dad is average the child will have to rely on mom’s Xs for intelligence, because the presumption is that dad’s X is “not smart”. Mom has two X chromosomes. She might pass on the smarter one. Or maybe she passes on the one that is not smart. Not to forget that during meiosis genes often do a little mixing so the child could get genes from either original X. Either way, a daughter could still get an average X from mom or a smart X. The guarantee of a smart daughter is less because you don’t know if mom has two smart Xs or just one which is dominantly displayed.
If the child is a boy, he will only get one X from his mom. None from dad. So in that case it would be the mother passing on intelligence. So you better hope he gets the best genes from her Xs when they undergo meiosis.
This is of course assuming that the X chromosome really does carry intelligence, that intelligence is dominant, and pretending that other factors and genes don’t come into play.
My convoluted point being: dad would have just as much say in passing on intelligence genes to daughters because he has an X chromosome which they receive. He might not have any say in his son’s intelligence.
A smart mom has two X chromosomes. One might not be carrying smart genes even if mom herself is smart. Her children could get an average X.
This is entirely based on these very specific rules of dominance and assuming the X chromosome is the only one that matters. This is probably not accurate anyway. Genes really aren’t that simple.