Fushimi Roku guessed correctly, Kujo Hikari's motive for murder did indeed stem from his father, Kujo Mutsumi, but it wasn't Kujo Mutsumi's direct instigation.
You see, Kujo Mutsumi is seventy-six this year, which, when you round up, makes him almost eighty. Not everyone at eighty has the energy to become the President of the United States. Kujo Mutsumi can feel his health declining, time is fair to everyone, and he has a premonition that he won't live much longer.
Previously, Little Wei came back home once for the sake of her daughter. At the time, Kujo Mutsumi urged for marriage, also out of necessity, as the Kujo Family had dwindled in numbers and all the major conglomerates faced a situation of having no successors.
Kujo Mutsumi even considered passing the position of Family Head to his daughter, letting Kujo Yua manage the Kujo Family, but after some thought, he gave up.
