Question: In general, nobody has an obligation to provide positive help to anyone else, no matter how great their need. There would seem to be one exception, in that parents have an obligation to provide for the needs of their children. Do they indeed have such an obligation? If so, why? And when does it expire?
Answer: Objectivists hold that parents are obliged to care for and raise their children. While Objectivism does not accept any unchosen obligations, it does recognize that one can, through one's choices, place another person in jeopardy. By creating a dependent child, the parents assume an obligation to see the child through to independence. Independence in Objectivist terms means being able to live as a rational being, on the efforts of one's own mind and body.
Exactly when the parents' obligation expires (or, indeed, strictly who has the obligation in the first place) are topics on which there are some reasonable differences of opinion. If you like, I could go into these issues in a follow-up. But certainly the obligation expires by the time of the child's legal adulthood. Indeed, the child's reaching adulthood healthy and able is the very goal the obligation must fulfill.
Of course, no one has an obligation to have children in the first place, although personally I think it is something to seriously consider, and that missing out on children can mean missing out on important values.
William R Thomas writes about and teaches Objectivist ideas. He is the editor of The Literary Art of Ayn Rand and of Ethics at Work, both published by The Atlas Society. He is also an economist, teaching occasionally at a variety of universities.