Little Eyolf tells the story of the Allmer family. At the outset of the play, the father, Alfred, has just returned from a trip to the mountains. While there, he resolved to focus foremost on raising his son Eyolf, rather than continue work on his book, Human Responsibility. Eyolf, though described as having "beautiful, intelligent eyes," is paralyzed in one of his legs, and thus his life is a sheltered one. He craves more than anything else to live the life of a normal boy, but his father knows that this is not possible. As such, Alfred wants to turn Eyolf towards loftier, intellectual pursuits.
The Allmer household is soon visited by the Rat-Wife, a woman capable of enchanting rodents into following her into the sea, where they drown. She leaves when informed that her services are unnecessary, and Eyolf follows her, unnoticed by Alfred, his wife Rita, and Alfred's sister Asta. Once Eyolf is gone, Alfred details his plan for being a better father to Eyolf and allowing him to attain happiness. In the course of his description, they are visited by Borghejm, an engineer, who is interested in Asta. While Asta and Borghejm walk outside, Rita's possessiveness of Alfred is revealed, during which she even wishes that Eyolf had never been born, as he diverts Alfred's attention from herself. Rita and Alfred's conversation is interrupted by the return of Asta and Borghejm, and then followed by sounds of shouts down by the sea, which reveal that Eyolf has drowned after following the Rat-Wife into the sea.
Down by the sea, Alfred mourns and is comforted by Asta. Rita and Borghejm follow, and once again Borghejm removes Asta from the action allowing for confrontation between Rita and Alfred. In the course of their conversation, Rita talks more about needing Alfred wholly while Alfred reveals that he married Rita in order to be able to better Asta's life. They also each blame each other for Eyolf's injury (as a baby, he fell off a table while they were making love), with Alfred accusing Rita of "luring me in to you," distracting him from his duty to watch over Eyolf.
Borghejm and Asta return, and Borghejm is once again unsuccessful at convincing Asta to marry him. However, when asked by Alfred and Rita to stay with them and take Eyolf's place, somehow allowing them to ease their guilt and avoid the problems in their relationship, Asta decides to marry Borghejm and follow him north. With Alfred indicating a continued unwillingness to be the husband Rita desires, she shares her new plan to try to better the lives of the poorer children who live down by the sea. In this, Alfred sees something positive again in Rita, and Alfred decides to remain, so that together they can atone for their mistakes.

Question: Why did Alfred want Eyolf to become an intellectual?
Answer: His leg injury would limit him.
Alternative answer: because he was paralyzed in one leg and couldn't lead a normal physical life.