Ok FYI:
White haired dude is ML and they are NOT related! Hes just calling him hyung as a way to show affection( you do that to a guy older than you).
Black haired lil bro is red haired dudes REAL brother that died once on a trip. MC is blaming himself for his little brothers death and uses white dude as a substitute for his death younger brother (he knows that, but doesnt wanna admit that, cuz he knows how bad it is to see his real younger brother in white haired dude).
White hair dude likes our MC, but until now our MC doesnt like him back( cuz he feels like he cant, cuz he has been using white dude as a substitute for his lil bro the whole time and cant see him as anything else).
White hair dude is actually an entity thats born from affection( according to how i understood it), he was once just a sword, and i guess his owner loved him so much that his affection got white hair dude reborn to a human. And probably our MC was that dude in a past life or he looks similar to him (but thats just my assumption).
Now back to why MC's family behaves so awkward?
The realize how they made MC feel responsible for the death of the youngest son in the family. They realize how traumatized he must have been, and that they realized that, when MC was having a nightmare about feeling guilty of his younger bros death. He yearns for the white hair dude, cuz he didn't make MC feel bad, he made him feel likr he's the same big brother he was once. So to redeem themselves, his parents send him to therapy. But cuz NO ONE WOULD FUCKING TELL HIM WHY, he run away. His parents were obv extremely worried about him and i guess they got in a car accident looking for him. Makimg MC now feel guilty about two additional deaths in his family.