In Igbo culture, family has a broad definition. Not only are Obi's parents and siblings his family, but all the men and women who come from his region are also considered his kinsmen. While on the one hand this means that Obi has a strong social network and support system, it also means that his web of obligations is broad. Obi ultimately finds his duties as a member of the Umuofia and as a member of his own family to be burdensome.
Because Obi has absorbed the western notion of the nuclear family, and because he feels contempt for much of his indigenous culture, he fails to recognize the Umuofia Progressive Union as an extended support system for him during his time of need.
Although Obi is willing to flout custom when it offends only his friends in Lagos, he is unwilling to choose Clara over his family, especially when he realizes how isolated he will be if he does so.