Peter Singer: "Characteristics like rationality, autonomy and self-consciousness...make a difference. Infants lack these characteristics. Killing them, therefore, cannot be equated with killing normal human beings."
This is an interesting issue to me because the script is kind of flipped. Both sides are making value judgments, but the left ultimately makes it a conscience issue where the right ultimately goes with science.
The left basically takes the position that the legal concept of "personhood" is not synonymous with being a "human being." You don't have rights because you are a "human," but because you are the type of human that society defines as a "person." Because the issue of personhood is inevitably non-scientific, involving subjective judgments about "rationality, autonomy and self-consciousness" and the value of life, and because the rights of another person (the mother) are inevitably affected, it is improper for the state to settle this "moral" issue. While individuals may believe in God and judgment, ultimately we each have to make up our own minds regarding such issues. The rights of the individual person to chose its own destiny must prevail over the rights of only a potential-person to live. An arbitrary, non-developmental line is ultimately drawn: once the baby is out of the womb, it is a legal "person" with its own rights. In the womb, it is the mother's body.
(Mr. Singer would not draw this arbitrary line and says that infanticide should be legal for the same reason he thinks late-term abortion is legal--not full-fledged humans yet--but this view is has been currently deemed abhorrent. Arguments have also arisen over the personhood of groups like slaves and invalids, and these have shaken out differently. Right now treating people of other races as non-persons is considered abhorrent, but we are re-exploring the question as it concerns invalids. It is also considered abhorrent to compare arguments about slavery with arguments about abortion.)
The general take on the right is that innocent human life (i.e., a human being that is not threatening another) cannot be intentionally destroyed, so the only question is when does human life emerge. It is true that there are marked differences between human beings at various points in their development. There is massive development that occurs between zygote and infant, but there is also significant development that occurs between infant and toddler, and toddler and adult (as Mr. Singer argues). Some may argue that it is unreasonable to label but all of these beings as "human" in their various stages of development, but ultimately one has to err on the side of caution when dealing with grave moral decisions. Because science tells us that a human life begins once a sperm fertilizes an egg and that a human person with all capabilities will inevitably emerge if nature is left to take its course (barring disease), there is really no absolute basis to draw the line elsewhere. Some might see this as over-restrictive, but it is more important to ensure that no possible humans beings are killed than to ensure that everyone agrees.
In the background on this side is a belief that right and wrong are real things and (traditionally) that people will be judged based on their decisions. Because murder is absolutely prohibited, the right of the baby to life is more fundamental than, and must prevail over, the right of the mother to choose.