Different conceptions of life in different contexts. Individual cells are alive in the sense that they can die, not in the sense that they are generally self-sustaining and worthy of care and protection.

When I bleed, red blood cells are streaming out of my body and dieing. Nobody cares about the sanctity of those cell's lives.

An embryo or fetus is certainly alive in the same way as any other cell in your body is alive. It is arguably not yet a life, or a human life though. It just isn't developed enough to have the features we associate with living beings. It's arguably just another part of the body, worth no more consideration than a tumor.

FWIW, whether or not an embryo or fetus is alive is irrelevant to the pro-choice case. It just impacts how individual people think about their own pregnancies. Forcing someone to carry a pregnancy against their will is still a violation of their most basic human rights. If that fetus needs protection, it can do so outside of an unwilling person's body.