My guess is that the father was trying too hard to please his wife and favor her and her son, thus ignoring Itsuki because she hated him. Or he's a soulless jerk who didn't love any of them and favored the younger son as an heir to save face after getting remarried, but also wanted the eldest son to take over...
Seriously? "Slut"? Then why didn't you call the father a 'slut'? I know, it's because he's a guy, right, come on, you can tell me! Actually, no, you can't.

ehh the lil bro ended up with that girl? the girl kinda gave off a slutty aura a bit
the maid n the big bro kinda made a weird couple luke they were licking each other's wounds
but um confused.... the wife died n the dad put the letter containing the will stating thr youngest gets everything in the coffin so does that mean he actually cared for the eldest son n had no intention of giving everything to the eldest? then why b such a attached father to the wife n youngest son n ditch the oldest son?