I have not read Singer's position on the issue until just now. His position is basically exactly the same as what I independently concluded (and still believe).
> He seems to accept that what most folks would call infanticide is okay
If you life begins at conception and abortion is never morally okay, you can skip reading my argument because I know it won't convince you; I'll see you in the footnote [1].
If you believe abortion is okay before a fetus is A weeks old, pick some X < Y < A. Two women are pregnant with fetuses of X weeks old. Alice gets an abortion at Y weeks (morally okay, according to you). Brenda gives birth at X weeks, then asks to have the baby euthanized at Y weeks (morally murder, according to you).
The only difference in the two situations is that Alice's child happens to live in her body, and Brenda's child does not. They are at the same stage of development otherwise. If Brenda's child has additional rights that Alice's does not, what are those rights based on?
My answer is that the law needs a bright-line test to determine what is or is not a person. Whatever test we pick should be easy to understand / perform (even for a layman), and there should be no false negatives (it's fine to forbid the killing of an organism that does not yet have the moral status of a person, and abhorrent to permit the killing of an organism that has the moral status of a person.)
"Birth" is an easy-to-measure bright line that already has some legal and historical backing (e.g. for establishing one's legal age for things like school / driving / tobacco use, we count since birth.)
So I would say infanticide of an infant that has the same level of personhood as a fetus is morally on the same level as abortion, which is morally on the same level as euthanizing a pet. Having infanticide be regarded as murder (legally) is an unavoidable side effect of trying to find an easy-to-test heuristic (has the person been born yet?) to approximate something with moral color that's hard to test (is this organism human enough yet that killing it is morally worse enough than euthanizing a pet that the parent should go to jail for it?) [2]
Your argument is basically a reductio: You have decided that infanticide must be defined as murder, and any moral system that allows it must therefore be thrown out. "Infanticide = murder" is "too far up the stack" to be used as a premise, especially if you're pro-choice. If you say "infanticide = murder, we must adopt a system that provides this outcome" then a pro-life opponent would say "abortion = murder, we must adopt a system that provides this outcome." It's basically that one weird trick that makes mathematicians hate you: If coming up with an argument is too hard, just make your desired conclusion an axiom; the proof is then trivial.
[1] I reject the premise that life begins at conception, as the arguments in favor seem to invariably rest on either an unmeasurable claim based on the "soul," or some religious authority. Government is in the reality business, and separation of church and state is an important principle. Therefore the premise is invalid for creating policy.
If you accept the premise, it seems to me that the pro-life side has an enormously strong case for its conclusion that abortion is murder. Despite the simplicity of the pro-life argument, I'm always astounded when I realize how many pro-choice people seem to be fundamentally, perhaps willfully, ignorant or incapable of logically addressing their opponents' position.
[2] The logic behind "innocent until proven guilty", and the entire legal/court system, is based on the same kind of thinking. You're trying to find an easy-to-test heuristic (was there a written law against something the person did, did the court system follow the rules of evidence and procedure?) to approximate something with moral color that's hard to test (did this person do something so bad that they deserve to be jailed or otherwise systematically punished?)
