If by "we," the speaker means the average person on the street, maybe that's true. It reminds me of things like this clip (warning: brief foul language). If "we" can't "name a country that start with 'U'" (various answers: Yugoslavia, Utah, and plenty of "I don't know's") or find Iraq or Israel on a map, then maybe popular opinion isn't the best.
But what about scientists? When do they say a new life begins? Turns out, that question is ridiculously simple: fertilization. Patrick Lee, director of the Institute of Bioethics at Franciscan University of Steubenville, and Robert P. George, professor of jurisprudence at Princeton University and founder of the American Principles Project, do an excellent job explaining the science here.
All of this is pretty common-sensical, to boot. For example, we know as a matter of undisputed scientific fact that:
Many amazing things happen at fertilization. Your baby's entire physical attributes are determined including gender, hair color, and eye color. Between days 7-10 from fertilization implantation usually occurs.
Assume for a moment that the baby's gender is male. We now have a living organism (which scientists call a zygote) which consumes food and secretes waste, it's growing, moving, and so forth. The cells are themselves quite obviously alive. And it's also a distinctly male organism. Even though we can't see the outward signs of it, the zygote is a boy zygote, and is genetically different than girl zygotes, and genetically different than the mother. He has XY chromosomes, she has XX chromosomes. To say that the zygote is part of her body is to suggest she's part-male. It's a silly and unscientific claim.
Of course, pro-choicers go much further. Even after the male fetus develops genitals, they'll keep arguing that he's part of her body, as if pregnant mothers suddenly develop two hearts, four lungs, and both male and female sex organs. And of course, they don't believe this themselves. After all, consider the so-called "therapeutic abortions," where children are killed for having conditions like Down's Syndrome. Doctors explain that the baby will have (and technically, does have) Down's Syndrome -- the mother doesn't. It isn't as though she suffers a brief spell of Down's Syndrome for nine months, before giving birth. So really, when it suits them, even pro-abortionists (and here, they're pushing for aborting the disabled, so the term fits) admit that the child is a distinct living being from the mother even when they're in intimate physical proximity.