There is a difference between law and morality. Law deals with efficient, practical ways of ordering society. Morality deals with good and bad. In the extreme, law is arbitrary. We go on green and stop on red. It could just as easily have been the reverse. In the extreme, morality is absolute. It is wrong to reject God. Other times there is an overlap of law and morality. It is both illegal and immoral to murder or steal.
Under our system of democracy, in order to preserve its integrity, law must be totally separate from morality. This allows for the practice and development of all moral systems. Strict adherence to this distinction is critical.
Without resorting to morality or religion, there is a viable argument for making human abortion illegal in many circumstances. The law protects us and our property so that we as individuals do not have to do so ourselves. Even the physically weakest person in society is protected the same as the strongest.
There is no one in society that is weaker than the fetus. Its very survival depends upon the good graces of another. The question is whether or not we should extend the protection of society to this our weakest member. The answer is clearly no, if and only if the fetus is not human.
It if is not human, then what is it? There is no question that it is some yet unfulfilled potential. But is this enough to make it human? The answer must be an unequivocal yes. Throughout our entire lives, as we grow, change and age; we are all some yet unfulfilled potential. There is no reason to distinguish the unborn.
While the fetus depends upon the mother for its existence, this is not without some effect upon the mother. This can range along the continuum from discomfort to death. In the extreme, the choice between the life of the fetus and the death of the mother becomes clear. The actual life of a living human being must be favored over the potential life of the fetus.
After this the choices become more difficult. Indeed selecting the chooser is the first hurdle. Is it the mother, the father, the doctor or society that makes the life and death decision for the fetus and the life altering decision for the mother? Remember the decision from a legal perspective is not a matter of right or wrong. Rather it is a matter of the efficient practical ordering of society, always remembering the purpose of law in society is to protect those who cannot do so themselves.
It seems clear that the law needs to protect the fetus in all situations except when it causes the death of the mother. This may seem harsh in the case of rape or incest, but from the fetus point of view, it matters not how or why it was conceived. Once the fetus has become emancipated from the mother, and particularly when its life has been dictated by the law, the mother should not be compelled to raise the child. Society, having protected the life must take responsibility for it until it can fend for itself.
The potential humanity of the fetus must have precedence over the convenience of the mother. The individual steps between the convenience of the mother and the death of the mother must be decided on a case by case basis, always with an emphasis of protecting what cannot protect itself. (Parenthetically this same reasoning can be applied to assisted suicide and euthanasia. But that discussion is for another day.)
Of course, the law cannot restrict a person's moral or religious belief regarding abortion. They are matters of faith and conscience and as long as acting on them does not conflict with law the are as they should be protected.