The philosopher Francis Schrag wrote a chapter titled Children: Their Rights and Needs in the book Whose Child? Children's Rights, Parental Authority, and State Power by William Aiken & Hugh Lafollette.
Schrag provides a summary of the aargument for causal parental responsibility:
The gist of this argument is this: people are responsible for the predictable and avoidable consequences of their actions. If two adults (recognizing the possibility that a helpless child might be conceived) have sexual relations and such a child is indeed born nine months later they are responsible for its existence and have to care for it. She later refers to Sidgwick's version of this argument, demonstrating that she is aware of other philosophical defences of the causal principle.
But Schrag disagrees with this principle. In an extraordinary paragraph, she throws the kitchen sink at it, firing off diverse objections in rapid succession. Each one of her objections could be the subject of an entire post. I will address just one here. Schrag states:
Why should a perhaps spontaneous act of love and passion which takes but a few minutes give rise to an enormously taxing and complex duty extending over perhaps decades?
She does not answer her rhetorical question but leaves it to stand as the objection. This is an argument from incredulity. Schrag is arguing that she can't imagine why doing a small thing should result in having a big responsibility. She is appealing to the notion that reality cannot be so unfair as to make one bear huge consequences for doing something short-lived and fun.
This argument is just a confession that the objector lacks the capacity to understand why something she views as insignificant can have significant consequences. It is the same objection to say "how can such a trivial thing as me exerting some pressure with my finger on a gun trigger be enough to make me guilty of murder?".
We live in a time when the actions of a few individuals could destroy human civilisation with nuclear weapons. Would we accept from them the defence that "surely merely talking and pressing buttons cannot make us responsible for so much murder"? It is an infantile objection.