I'm personally against abortion unless the mother's life is in danger and in cases of rape (although I think adoption should be the first choice if possible). If it's a health issue and abortion's the only option, then a mother should be allowed to do it.
As for why, I'm going to propose an argument that I don't hear very often, and this is just my opinion.
When a mother becomes pregneant, it doesn't matter when the fetus actually becomes a living human. Regardless of when or if the fetus is alive at a certain point, it always has the potential to become alive, and to become a human being. By aborting the fetus, regardless of when you do so, you're denying it the opportunity to one day become a complete human.
Does this make sense to everyone, or do I need to clarify?