Here's Professor Singer:
My understanding is that it is not until after the first birthday, so somewhere between the first and second, I think, that they typically recognize the image in the mirror as themselves...Really, I think this is a gradual matter.This is the slippery slope onto which the liberal view of abortion rights leads us. Once we deny that an unborn child should be considered a person we soon lack any basis for holding that born children are persons - at least until they become self-aware - and if it is the mother's right to terminate the life of an unborn non-person, it will eventually become her right to terminate a born non-person. Just as we have unwanted pets put away, so, too, will there be a demand for the right to put away other unwanted non-persons. Where does it end?
If you are not talking about public policy or the law, but you are talking about when you really have the same moral status, I think that does develop gradually. There are various things that you could say that are sufficient to give some moral status after a few months, maybe six months or something like that, and you get perhaps to full moral status, really, only after two years. But I don’t think that should be the public policy criteria.
He doesn't think that this should be a public policy criterion because if it were there'd be no moral constraint on killing children up to two years old just as there's no constraint today on killing them while they remain in the womb. Even so, Singer does advocate making infanticide legal up until a child is about 30 days old.
One would like to ask Professor Singer why self-awareness should be the criterion that confers "full moral status". Why not the ability to communicate, or to ratiocinate, or to do algebra? If self-awareness is to be used to separate persons from not-quite-persons are individuals in a coma sub-persons? If so, do they forfeit their right to life. If they do not, why not?
If the answer is that they have the potential to come out of the coma and be self-aware why does not the same apply to the unborn?
This is why advocates of an unrestricted abortion license long ago gave up trying to defend their position by arguments. They simply don't have any. All they have are slogans and the power, through the federal judiciary, to impose their will.