The “life begins at conception” argument is really a statement of the theological position that the human soul begins, or the fetus is endowed with a soul, at conception. Thereafter, the thinking goes, the embryo is a human being with human rights.
Since the “soul” doesn’t have any standing in law, and not all religions and sects agree, “life begins at conception” is the meme of choice.
But, if an embryo or fetus is a human being, it is a person. In some aspects of law, it is just that. Many states have fetal homicide laws, for example.
And, if the fetus is a person, killing it is literally murder.
Protecting a person from murder is not solely a religious duty, it is a legal and moral one.
That the pro-choicers don’t see that is their biggest weakness. They think that they’re up against religious fanatics and they can’t engage with the logic of the pro-life case.
That’s why, although “pro-choice” has a majority in the polls, there is also a majority in favor of dramatically restricting abortion.