We should stop using this argument, it doesn't matter. Let's discuss why. First, life doesn't "begin" anywhere. Life continues. A baby doesn't magically come alive the second it's born, nor is that status granted on it any time between conception and birth. Indeed, the component parts of the fetus - the sperm and the egg were already alive before they merged. Those cells came from other living cells, and in the mother's case, the eggs were created LONG before she even had sex, much less became impregnated or gave birth. The idea that life begins anywhere is a false yardstick, and it only hurts the cause of pro-choice.
Instead, it's important to focus on the rights of the individuals involved. Roe v Wade said that laws against abortion were a violation of a woman's rights granted by the fourteenth amendment. That amendment says:
No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
This has evolved into the concept of bodily autonomy. To put that simply, a woman has a right to do what she wants with her body. Even if that means the life or death of another human being, born or unborn. Just like I can't force you to give up a kidney to me if I'm dying of kidney failure and you're my only match. It's pretty straightforward, actually.
Of course, the common response to this, and the one that I received in a conversation that lead to the writing of this post is, "but what about the baby's rights? Doesn't it deserve to live?!?" Well, sure, but not at the expense of the mother's rights. That's the way all of our rights work. I have the right to free speech - right up to the point that that speech impacts another person. I have the right to keep and bear arms - right up to the point that I use those arms against another person. I have the rights to life, liberty, and the pursuit of happiness, right up to the point that it affects another person's rights of life, liberty, and their own pursuit of happiness. The baby has rights, but if the baby's rights affect's the mother's, then the mother's rights win. "but, aborting the child affect's the baby's rights too!" Yes, you're right. But look at it this way - If I decide I like your house, and I move in, am I breaking a law? yes, obviously. it's YOUR house. Of course, kicking me out of your house violates my rights to life - If I'm homeless, I'm likely to die without a place to stay. Of course, that's not your problem, your house is yours, and I have no claim to it, therefore your rights trump mine. Well, the same argument applies to the woman in question. She has a right to her body. Saying she has MUST give up that right because there is a child inside it is the equivalent of suggesting that you MUST give up your own right to property because a homeless person has decided they live there now.
This is why the "when life begins" argument is irrelevant. Life is always there. Abortion isn't a question of life, it's a question of rights.