Taken me ages to get this started again, but I thought I might as well have a bash...
Matrilineal- Inheriting or determining descent through the female line.
The Pureblood Society was a patriarchal one. It always had been. It always would be.
A father's name and approval meant everything. As did sons. They were the ones who could carry on the line into the next generation. Daughters meant nothing, or next to nothing. They were mere vessels to carry on a bloodline.
Sometimes, when he looked at his eldest daughter, Lord Cygnus Black regretted that this was the case. Bellatrix was such a firebrand, yet still so pure and loyal and….worthy. A perfect heir, if not for her gender. So yes, sometimes he regretted it.
Only sometimes.