There's some tension in feminist thought regarding paternal responsibility. On the one hand, feminists typically hold that a pregnant woman has absolute discretion over whether to get an abortion or see the child to term, with no obligation to consult the father or consider his wishes. Yet if the woman chooses to have the baby, the father is held responsible and made to pay child support. This seems unjust.
To be held responsible for an outcome, one must have some control over it. The father certainly shares responsibility for the pregnancy (assuming he had sex voluntarily). But since childbirth in the feminist utopia depends upon failure to abort, one can only be responsible for childbirth if one is responsible for a failure to abort. And if the decision to abort or not is made without so much as consulting the father, one cannot plausibly hold him responsible for it. If abortion is accessible (in the broadest sense of the term, including moral and emotional considerations, etc.) to the mother, but she unilaterally decides against it, then her continued pregnancy is her responsibility and hers alone. She could have avoided it, but chose not to. It would be unjust for her to force others to pay the costs of her decisions.
Now, Dr. Pretorius makes the obvious point that the child's welfare matters here too. I certainly wouldn't deny that. But amongst all the snarkiness he doesn't seem to have noticed that this doesn't actually help his position any. That a child has the right to be adequately provided for does not in itself entail who has the burden of fulfilling this right. Presumably the burden falls on those who are responsible for bringing the child into the world -- with social welfare as a 'safety net' if required. In the case of the unilateral feminist described above, it was the mother who was solely responsible. If she is too poor to adequately provision her child, the state should step in and help (for the sake of the kid, who should not be punished for his mother's selfishness).
Pretorius actually suggests the more specific principle:
(P) Children have the right to be [financially] supported by their biological parents.
This is not plausible. Suppose a mad woman extracted sperm from you whilst you were sleeping, and used this to get herself pregnant. Nine months later, the bills start arriving, demanding that you pay for this child that you never even knew you had. Are you obliged to pay them? If the mad woman is married, and the otherwise sane couple are taking good care of the kid, does the child really have a further right to be financially supported by you in particular? Is he somehow harmed if the money comes from somewhere else instead?
Or, less fantastically, consider a case where the father is a rape victim, and ask all those same questions. It seems clear that if someone is manipulated into becoming a biological parent against their will, then they are not responsible for the child, and hence it would be unjust to hold them responsible by forced child support payments. That's not to deny the child's basic rights to welfare. It's just to deny that the manipulated victim is the one who has to fulfill them. If a general welfare right cannot be adequately fulfilled by those responsible, then the burden passes to society as a whole (social welfare), not any particular non-responsible individual.
The crucial question now is whether the father in our original "unilateral feminist" scenario was "manipulated into becoming a biological parent against [his] will". As previously noted, it's crucial here whether abortion is "accessible" to the mother, in the broadest sense of the term. Given the normal progression of things, being responsible for conception typically suffices to carry over into responsibility for the consequently born child. But if abortion is a live option, then childbirth is not just a consequence of conception. It's a consequence of conception plus the decision not to abort. If the man is excluded from the latter decision, then he cannot be held responsible for it.
So, we should reject (P). Indeed, quite apart from the unfair attributions of responsibility, it's a pretty ludicrous right in its own, uh, right. From the point of view of the child's welfare (which Pretorius purports to be concerned with), what matters is that his needs are met. It does not matter who meets them. So (P) is not really about the child's welfare at all. It's about holding the father personally responsible. But that's something that feminists cannot reasonably do if they want to exclude the father from prior important decisions.
One might object that some of the child's needs are special in the sense that they can only be met by the biological father. This is obviously false concerning financial needs: child support payments are not intrinsically more valuable than social welfare payments of the same amount. But it is more plausible in connection to emotional needs. Perhaps fathers have a moral obligation to love their children, no matter the circumstances of the birth. (Though I think in at least some cases this would be an unreasonable demand, as the prior examples make clear.) Regardless, this cannot be a legal obligation -- you can't sue people into becoming good fathers. Forcing money out of them certainly won't help.
In fact, considerations of the child's welfare should lead us to reconsider paternal exclusion from the decision not to abort. The unilateral feminist is intentionally bringing into the world a child who will have an uncaring father. That seems at least somewhat irresponsible. If she could abort it and instead (say) have a child a year later with a more dedicated father, that seems clearly preferable from the next generation's point of view. (Indeed, it seems preferable from everyone's point of view, assuming feminists are correct about how harmless abortion is.)
Dr. Pretorius attacks unwilling fathers by saying: "you know, sometimes you don't just have the right to do whatever you want regardless of how it affects other people." Yet in the immediately preceding sentence he was insisting that a woman has the "right" to carry her baby to term, no matter how this affects the father (or, presumably, the child itself). Very ironic.
Bringing a child into the world is a very serious undertaking, and can be a significant burden for those who do not welcome it. Recognizing this, feminists embrace abortion for the choice it affords women, allowing them to avoid this burden. But why are men deprived of the same choice, the same chance to say, "No, I'm not prepared to accept this responsibility right now"?
Doesn't it go against liberal principles to allow one person to unnecessarily burden another against their will? If so, then men - just like women - cannot fairly be burdened with an unwanted child. Either the child can be brought to term without incurring rights against the father, or else the father too should be allowed to abort it. (The former sounds more plausible.) For feminists agree that, even post-conception, a child is an unnecessary burden. It may be aborted if that would be most convenient for the woman. It seems plain sexism not to extend the same courtesy to men.