Based on your argument, blood donors are on the hook for supporting any children whose life they saved.
Tell me, where and when do the responsibilities of fatherhood actually arise? Or, by your accounting, is there even such a thing as paternal responsibility? It cannot arise from "choice to be a father," no more than motherhood's responsibilities arise from "choice to be a mother."
This is one of the main reasons why abortion is such a radical and repellent evil: because it kills the child, yes: but this killing is predicated on the premise that "I, who have conceived, did not choose to conceive this child, and I never intended to shelter it in my womb, give birth, or parent it." All irrelevant. The child once begotten/conceived has natural rights, and these begin when its life begins: the rights to the protection, nurturance, and support of its natural parents.
A man who says "Not my problem, I didn't choose it" is an aborter at heart --- whether the baby survives its gestation or not --- because he holds the same hell-proposed premise : "It has nothing to do with the objective fact that I am the begetter, it's all about my choice."
Based on your argument, blood donors are on the hook for supporting any children whose life they saved.