Al, a single father of young Beth, found himself destitute. To give Beth hope for a future life, he agreed to have Charlie adopt Beth. Charlie was much better off than Al, and as far as Al could tell, was an excellent prospect for fatherhood. Unfortunately, soon after the adoption, Al and Charlie's fortunes reversed. Now Charlie was destitute while Al was well off. Charlie approached Al, suggesting that perhaps Al could re-adopt Beth. But Al said: "She is your daughter and no longer mine, and hence the responsibility is yours." Charlie further asked for financial help for Beth, indicating that he and Beth's health was poor and he (Charlie) could not afford the treatment she needed. Al responded: "Beth is not my daughter. Thus, while her misery has a call on me, it no more has a call on me than the misery of my other people I come in contact with. And I am already sufficiently contributing to the alleviation of the misery of other people, by giving most of my income and available time to various organizations that work with the needy in the city. Moreover, my doing so is financially more efficient. Beth's medical needs are particularly expensive. For the cost of alleviating her misery, I can alleviate the misery of two other poor children. Of course, if Beth were my daughter, her needs would take priority. But she isn't—she's your daughter."
Unless you're a utilitarian, and perhaps even if you are, I think you will share my strong moral intuition that Al is doing something seriously wrong. There are two aspects of this wrong. First, we assume that Charlie has done something good to Al when Al was in need—he took on Beth—and Al is being ungrateful. But we can tweak the story to make Al owe no gratitude to Charlie. Perhaps Al had already done as great a good to Charlie, or perhaps Charlie took on Beth solely for the sake of a tax break and Al was initially mistaken about Charlie's motives.
Second, Al owes more to Beth than he owes to other needy children. Adoption does not, then, completely negate parental duties. In fact, many onerous duties remain with Al, conditionally on Charlie being unable to fulfill them. Beth is not a stranger to Al. I do not know whether we should say that Beth is Al's daughter, but even if she not Al's daughter, the relationship that Al has to her is sufficient to ensure that he is morally responsible for her needs in a way in which he is not morally responsible for a stranger's needs.
But now Al's relationship to Beth is that of merely biological father. This means that the relationship of merely biological father is sufficient to trigger serious duties.
And this, in turn, makes giving sperm to a sperm bank seriously morally problematic. For by so doing, the man is consenting to being the biological father to many children. Given the numbers, it is not unlikely that some of these children will not have their basic needs—whether emotional, intellectual, spiritual or physical—met. In those cases, the donor would have a serious responsibility for meeting these needs. But this is a responsibility he cannot fulfill since he does not even know who these biological children of his are. Therefore, by donating sperm, the donor has consented to a situation where it is likely that he would be failing to meet his serious responsibilities, and where he cannot even seriously try to meet his responsibilities due to confidentiality rules. And that is, surely, morally problematic, even if we bracket all the other problematic aspects of sperm donation.
Notice that any statistics to the effect that adopted children have their needs as well met as biological children will not help here. For what generates the problem I am now discussing are two things. The first is the man is apt to gain many biological children whom he does not know about, adopted into many families, and it is quite probable that at least one of these families is not going to meet the childrens' basic emotional, intellectual, spiritual and/or physical needs. Thus it is rather more probable that he will have responsibilities he is not fulfilling than if he just conceived several children with a woman he was married to, since in the latter case there would only be one family to worry about. Second, in the sperm donation case, the man has responsibilities he cannot even seriously try to fulfill, and that seems a very unfortunate situation.
This improves on an argument I posted a couple of years ago.