As I follow it, the premise that makes the logic work is that zygotes are people who are treated as not human. Therefore, other groups who have been treated as less than fully human should sympathise and protect them, quod erat demonstrandum.

But it's a wonderfully handy premise, because you can apply it to any group that's ever been victimised. Jews? Check. Native Americans? Check. Women? Check. In fact, since right-wingers reckon that white male christians are the most persecuted of victims, there's hardly anyone you can't sign up that way.