- Lore -
When Kaigaku became Uppermoon, he was number 6 like Daki & Gyutaro so they let him join them making their duo become a trio
Kaigaku became a demon before Zenitsu met Tanjiro meaning Jigoro is dead and his mental health is at an all time low.
Kaigaku has a different moral system compared to the siblings because he doesn’t really kill demons slayers but try to knock them out instead and put them somewhere so they won’t get eaten by the demons Muzan makes with his potions.
He doesn’t even want to eat or drink the blood of normal humans that the Ryoshi brings back, so he goes out on his own and finds horrible people that he can bring back and eat.
The cooks even let him has his own freezer so he could put the humans he found in there and when he hungry, they get it out of the freezer for him.
While Daki & Gyutaro see slayers as dogs who will just do anything their master says with no complaints at all. So they kill them with no hesitation and make their bodies look unrecognizable when their done.
Kaigaku thought he could never be friends with them until he saw them giving food & clothes to families & children who lived in poverty in the entertainment district.
Meaning it seems the siblings has a grudge against the corps for some reason, not humanity as a whole.
Maybe, all the Uppermoons have some unexplained beef with the corps.