In Things Fall Apart, Okonkwo feels ashamed of his son Nwoye in Part I of the novel and betrayed by him in Parts II and III.
In Part I, Okonkwo's greatest fear is that Nwoye will become like his grandfather Uneka, a titleless and effeminate male (agbala). Certainly, Nwoye seems more attracted to his mother and the arts than he does the uber-male culture of yam farming, wrestling, and war. Luckily, Ikemefuna comes along and becomes a surrogate brother to the boy, instilling in him the virtues of manhood. However, after Nwoye realizes that Okonkwo is the one who kills Ikemefuna, the boy disowns his father. Or does Okonkwo kill Ikemefuna to spite his own son?
In Parts II and III, Okonkwo hates his son for betraying the tribal culture in favor of the white colonial religion, Christianity. Okonkwo refuses to engage the boy as to the reasons of his conversion; if he had, he would realize that Nwoye has long been bothered by the tribe's practice of killing twins and other foreigners (Ikemefuna) and outcasts. Regardless, Okonkwo's fear is realized, as Nwoye becomes the titleless male whose conversion, among others, helps to break apart his family and, over time, unravel the culture of the Igbo.
Okonkwo believes that Nwoye is a disgrace and has turned out like his father. Okonkwo was deeply ashamed of Nwoye when Nwoye decides to join the missionaries. Okonkwo who has been raising Nwoye up since young to be perfect and to become one of the strongest man of the clan would of course be deeply ashamed when Nwoye cuts off his ties with the village.