Mary Elizabeth Williams declares herself a pro-choice liberal, but wants to concede that "life begins at conception". To her, this is undeniable common sense. But in fact, there is actually a very solid reason to doubt that any human's lifespan starts as early as conception. At conception, what exists is a single-celled zygote. That zygote contains the makings of not just the embryo (fetus, etc.), but of all the structures that will support the embryo (fetus, etc.)--the placenta, amniotic fluid, etc. Imagine (only somewhat analogously) a very full box you take off the shelf at Ikea (with great effort!). The box contains the makings of a bed, but also instructions, tools, packaging, styrofoam, etc. You take it home and put together the bed, discarding everything else. Would you say the bed started its lifespan as the full box? No, of course not. There is no bed until a bed has started to take form and become separate from everything else that was in the box. And at the point, it really makes no sense to say "the bed was once the full box."
Likewise, once an embryo has become differentiated, a few weeks into gestation, it would make no sense to say it started its lifespan back when there was just a zygote. The zygote is analogous (somewhat--this is not a perfect analogy) to the full bed-box. It's a forerunner of the embryo and all the support structures. I think the very common idea that life could start at conception stems from ignorance about what a zygote is. It's not an embyronic human being yet. It's a kit for making a human being, including components for housing, protecting, feeding, etc. You might be able to convince yourself that you were once an embryo (I think this is an intelligible position), but it really makes no sense to think you were once a zygote--a people-kit. No you weren't! You came from a people-kit, but you weren't one. It's much like in the bed/box example: the Ikea bed came from the box, but beds don't start their careers being boxes. No equal sign would make sense up there, between the box and the bed, and no equal sign would make sense between a zygote and an embryo (or fetus or baby).