The following quote indicates clearly why Okonkwo found it necessary to beat his young son:
Okonkwo ruled his household with a heavy hand. His wives, especially the youngest, lived in perpetual fear of his fiery temper, and so did his little children. Perhaps down in his heart Okonkwo was not a cruel man. But his whole life was dominated by fear, the fear of failure and of weakness. It was deeper and more intimate than the fear of evil and capricious gods and of magic, the fear of the forest, and of the forces of nature, malevolent, red in tooth and claw. Okonkwo's fear was greater than these. It was not external but lay deep within himself. It was the fear of himself, lest he should be found to resemble his father.
Okonkwo would therefore do everything in his power to ensure that Nwoye, who was to carry his name and legacy, shall never come to represent Unoka, Okonkwo's father who, because of his tardiness, brought shame to his family.
The following quote further emphasises Okonkwo's concern in this regard:
Okonkwo's first son, Nwoye, was then twelve years old but was already causing his father great anxiety for his incipient laziness. At any rate, that was how it looked to his father, and he sought to correct him by constant nagging and beating.
Since he was a dedicated, hard worker who wanted only the best for himself and his family, Okonkwo had the same expectation of his son:
Okonkwo wanted his son to be a great farmer and a great man. He would stamp out the disquieting signs of laziness which he thought he already saw in him.
Okonkwo was very firm and told Nwoye:
I will not have a son who cannot hold up his head in the gathering of the clan. I would sooner strangle him with my own hands. And if you stand staring at me like that," he swore, "Amadiora will break your head for you!"
When Ikemefuna was placed in Okonkwo's care, he and Nwoye built an almost inseparable relationship. Ikemefuna taught Nwoye many new things and Okonkwo noticed a change in his son's attitude. In his eyes, Nwoye was beginning to behave much more like a man, and this brought Okonkwo great pleasure.
Okonkwo was inwardly pleased at his son's development, and he knew it was due to Ikemefuna. He wanted Nwoye to grow into a tough young man capable of ruling his father's household when he was dead and gone to join the ancestors.