This argument is usually used specifically to argue against late term abortions. The assumption is that at the point that at a fetus has developed the brain structures necessary to support conscious thought – minimally at 28 weeks– the fetus is now in every way morally equivalent to an infant and aborting a fetus at this stage is equivalent to murder of a baby. (This is also the view of many pro-choice campaigners who argue that abortion rights should end at a certain point during the pregnancy, often at this point or at viability.)
The issue with this reasoning is the same as with the potential argument; it confuses the potential to have an initial conscious experience with actually having conscious experiences. Conscious experiences don’t just occur when the neural circuitry required for them has developed. Rather, conscious experiences require both neural circuitry and psychological stimulation from the environment (with the latter occurring through interaction with both a caregiver and the environment.).
Is there reason to think that birth is the point at which conscious experiences begin? We know that the uterine environment continuously sedates the fetus,in a state described as a “deep, dreamless sleep”. We also know that the initial wave of norepinephrine released at childbirth shocks the infant into consciousness, and that within less than an hour after birth, infants are interacting with and imitating their caretakers. If we must have a cutoff point for endowing personhood, the most ethically reasonable and scientifically-backed point is the one at which the baby awakens and begins to experience life, at birth.