I might miss the point, but the height is dependent on both parents genetically, so just comparing mothers with daughters is a bit like the usual "correlation does not equal causation" thingie, or not?
That's exactly what this is showing. The x axis is the fathers height and the y-axis the mothers height so you see daughters change of being taller going up when their dads are bigger. For sons the chance of being bigger than their father goes up with tall mothers.