The problem, of course, is that a Mother and her child are not strangers to one another. It would be unjust to insist that you keep a stranger alive at great inconvenience to yourself. It is not unjust to insist that you keep your own offspring alive. In fact, law, custom and morality all insist that we do keep our offspring alive.
You don’t have to take in the homeless man on the corner merely because the night is bitter cold. But if you lock your child out on the same night, you’re going to jail.
The Professor’s argument is nothing more than a non sequitur in fancy dress.
Actually another rebuttal is even stronger than yours.
The infant’s situation is *created* by the mother!
The infant did not put himself in the situation that would require sustenance from the mother. The mother did.
The analogy would be if you, hit somebody on the head that put him in a coma, and it just so happens that your blood is also the only one is the world that matches his so you are the only one who can keep him alive. Do you have a moral obligation to hook your body to his to keep him alive for the 9 month it takes for him to come out of the coma.
Even common law recognizes this. This is normally no duty to rescue someone else, except if it’s your action that put the person in danger, in which case there is a duty to rescue.
Something else to consider -- if for some reason, a stranger got hooked up to a life support system in your basement, you would not be allowed to pull the plug.