hi clo,
the abortion argument is at root one between competing moral and political assertions.
so long as folks decide their own assertion (life is sacred, only women choose) is inviolable, there's no pathway to a resolution in law which will make either side completely happy.
in the end, we bodge together a compromise, which begins with women's absolute right to choose at one end of the pregnancy and ends with the baby's absolute right to life (assuming medical sustainability) at the other. the conversion from the one to the other occurs along the journey.
csl appears to be asserting that the right to life begins at conception. there's no means to disprove it because it isn't a claim which relies on evidence - it's a religious claim based on a particular definition of what life is. he believes this as an irreducible truth. others don't share it. your belief in a woman's right to choose what happens to her body is fairly similar, although not identical.
for myself, i think rights conversations tend to end up with someone telling other people what they can't do. such things depend on one's perspective. libertarians often believe that in such circumstances, the government shouldn't involve itself except to protect an individual person's freedom. but of course, csl also assigns personhood to the foetus.
for myself, i don't really believe in irreducible truths (except the truth that truths aren't irreducible), and i also believe that the universe is naturally paradoxical (a second irreducible truth, which itself is paradoxical, ain't it). which means that issues of this type are doomed to involve competing principles. the best answers are usually also somewhat hypocritical in a paradoxical universe.