Establish a couple of counter-examples: Suppose a women puts out eggs that (for whatever reason) are only receptive (or more strongly receptive) to X chromosome sperm? Or that environmental conditions (perhaps related to what the chick eats or just her own genetics) in the vaginal canal give a mobility DISadvantage to Y chromosome spermatazoa? In both those cases, the guy's X:Y carrying sperm ratio could favor a male child, but after the maternal factors applied, a female child is more likely. Other alternative models easily could be developed. In order to say that "the male chooses sex" all these have to be DISPROVEN, which is pretty tough. I don't think that has happened, and in contrast, there is some evidence suggesting a (not well understood yet) maternal role.

This isn't my line of expertise. Maybe the effect is very small or it's not present entirely, but the point is that the presence of the X/Y chromosome in the male gamete, doesn't completely preclude some female involvement in sex selection. You need to think a little more logically.

from the text...
"The conventional wisdom is that the father’s sperm is the main determinant of the sex of a child. But increasingly scientists have found hints that maternal factors might have an influence too. For example, earlier work has suggested that single mothers are more likely to give birth to daughters."
"The idea of diet influencing sex ratio is already part of traditional wisdom. Folklore says that mothers should eat more red meat and salty snacks if they want a boy, and fish, vegetables, chocolates and sweets if they want a girl.
'This is interesting, since meat raises blood sugar for a sustained period of time, whereas sugar-based snacks raise blood sugar very high, but for a short amount of time, followed by a slump in blood glucose,' says Cameron."
If I had to guess, they may be positing that a female's blood chemistry effects the odds of a male sperm giving up its Y during zygote formation. I don't remember much about it though.

Sweets and chocolates would raise blood sugar faster than would a burger, simply based on the fact that they would melt to be liquid and the glucose would spike faster.

You know it's true.