The reason for the distinction at birth is the nature of the child until it leaves the whom. Until the child leaves the womb it is by definition a parasite on the woman. Although we often (are rightly) give a baby in the womb more affection that we give parasites, it doesn't change the fact that the embryo is "forcefully"(not sure this is the right word) making use of the mother's body, which makes the embryo by definition a parasite.
In addition, even today the process of child birth can be a dangerous process. Child birth constitutes a potential threat to a women's life that she, at any moment, may choose to forgo. You cannot put the potential life of the embryo in the womb above the actual life of the mother, no matter what stage of pregnancy she is in because at every stage she faces the future ordeal of childbirth.
Also, to disregard late term abortions because they are rare or because someone "should know by then", strikes me as naive. A lot can happen before you give birth that would make you decide not to commit to raising a child. Suppose the father or other care giver runs off dies. Suppose a new law is passed that requires babies to be raised by the state. Suppose.... anything. Until the child leaves the body of the mother, she is committed to nothing.
