Many prefers Asagi and Kojou because of the age gap of Kojou and Yukina. Moegi aside, Kojou always relies on Yukina. We cannot be sure that Moegi, Asagi's daughter, is a vampire like Kojou. If the king is Kojou, thqt makes the blood partner the queen.
Also, Yukina is the blood partner of Kojou. Lord Vatler said it himself to La Folia at the ending of episode 8, season 2. It also said that the priestess of cain is the princess of the fourth progenitor. At season 1, Kojou only refers Asagi as his 'friend'. She also has the holy sword like Sekkarou. Kojou and Reina call Natsuki Minamiya, 'Natsuki-chan'. She is also a vampire like his father, Kojou.
Another is Kojou never wants Asagi to know he is the fourth progenitor. Why? Watch all the into and outro of each episode. For me, it would be Himeragi Yukina and Akatsuki Kojou.