There is a good article at the IEP by Brynn Welch on filial obligations. Welch identifies several theories of filial obligation: that it arises from debt to our parents, from friendship with our parents, from gratitude to our parents, from reciprocity with regard to the goods specific to the parent-child relationship, from gratitude over such specific goods. One thing that I think would have strengthened the discussion is the recognition that perhaps we have lots of different kinds of filial obligations.
Take Aquinas, for instance. Aquinas thinks that children owe their parents a debt. (It is not what Aquinas calls a legal debt, which is what is assumed in what Welch calls Debt Theory, but what he calls a moral debt, which is a looser term.) But what we owe them are things like gratitude and respect. Aquinas is also an Aristotelian, though, and thus he thinks that parents and children are friends (one of Aristotle's paradigmatic examples of friendship is friendship between mother and child). And I doubt Aquinas is really unique here; the categories are too broad here, and the assumption that all our filial obligations are of only one type, required by the critical examinations of each theory, seems very controvertible.
Indeed, the parent-child relationship itself seems to be more of a family of relationships than a single relationship: a parent gives a child life, educates the child, plays with the child, is the confidant of the child, provides goods for the child, plans for the child, and so forth. In each case the parent has the role of parent and the child has the role of child, but the ways the two relate are very different. Each way of relating, though, seems to raise different questions with regard to obligation.