The fundamental disagreement in the abortion debate is the question of when a cluster of cells becomes a human being. Human development begins once the egg cell and sperm cell combine, but is this a fair measuring point from which you can call something a human?
People legally become adults at 18, but we'd be kidding ourselves if we said that they're a child one day and an adult the next. The same belief can be applied to human development. The point when the sperm cell and egg cell do not make the cell cluster a human instantaneously; it's still a cluster of cells that is invisible to the naked eye and bears absolutely no resemblance to a human being. It feels no pain, has no thinking ability and will not do these things for a considerable amount of time.
I think late-term abortions should not be allowed for the sake of convenience, but almost 90% of abortions take place during the first trimester. If we're to establish a guidelines based on logic and not our own personal ethics and morals, then I think a good bright line is the point at which a fetus develops sensory functions and thinking ability. The argument that stopping the development of a cluster of cells, which are a tenth the size of my fingernail, constitutes murder makes little sense to me.