I don't think it's a misunderstanding. Rather it's immense guilt. Looks like his psycho dad had kidnapped Ilwoo for a ransom while little Baekhee could only helplessly watch. Knowing his trauma related to his father I don't think all the guilt is gonna help him open up to Ilwoo.
If baeke gona leave ilwo just because of some misunderstanding (again) im gona fucking explose