I've recently met a pro-choice blogger by the name of Deanna Young, who runs a blog called Restringing the Violinist. She has written a couple of articles defending the right to refuse argument, one in which she has linked to my article, so I'd like to take the time to respond.
Forced blood donation analogy
In the first argument I'd like to respond to from her article explaining bodily rights to pro-life people, she formulated the following thought experiment in an attempt to be less "weird" than the Thomson's violinist scenario:
"In September 2013 a 72 year old man onboard a cruise ship required a life-saving blood transfusion. In order to save his life an urgent announcement was made asking crew members if they would be able to donate. Over 40 crew members ended up responding to the announcement. I'd then ask the pro-life person I'm talking to if they think what the crew members did was a supererogatory act (something good to do but not evil to refuse) or not."
I would agree that what the crew members did was supererogatory. They were not morally obligated to donate blood to the man who needed it. Having established that, Ms. Young then modifies the thought experiment as follows:
"...suppose nobody volunteered their blood and in their desperation three of the mans [sic] family members kidnapped you. While you were unconscious they attach you to a device that removes blood from your body and puts it into his. When you regain consciousness a doctor tells you that in order to save the mans [sic] life you will need to come in and donate regularly for the next nine months."
So this thought experiment is similar to the violinist, but a little more down to earth since it's a blood transfusion that's being forced and not being hooked up kidney-to-kidney with a famous unconscious violinist. She notes four parallels to pregnancy: One, that one person requires another person's body to survive. Two, the person whose body is being used does not want to be used in this way. Three, we are assuming both people have a right to life. And four, if one person decides to discontinue care, the other will die.
These are certainly parallels to pregnancy, but in this case it's the differences that matter. The reason that so many pro-choice thought experiments are flawed is because they remove one key piece from the moral equation: the person's responsibility. In the vast majority of pregnancies, the man and woman are responsible for the child's existence in a naturally needy state. Any thought experiment which doesn't have the "kidnapped" party voluntarily committing an act will be leading us in the wrong direction. As a result, the intuitions in these thought experiments are misleading. Otherwise you're just talking about pregnancies in the case of rape, and the responsibility objection obviously doesn't respond to rape cases. If we change the "kidnapped" person into, say, a mugger who inadvertently cut the 72-year-old man and caused him to bleed out, even if he wasn't intending to cut the man, I believe he absolutely would have a moral obligation to donate blood; in fact, I would say he should even be legally compelled to do so.
Car Accident Analogy
So in Ms. Young's second article responding to the responsibility objection, she has given two thought experiments to show that "having done a voluntary action that causes someone to need you to survive does not mean you should be legally obligated to sacrifice your bodily autonomy for their benefit even if you are morally obligated." Do her thought experiments do the work she needs them to do?
Well, the first thing we need to keep in mind is that the responsibility objection is not just the position that she causes the child to be in a naturally needy position, but that she caused the child to exist in the first place (and of course the man shares responsibility, but as this is about bodily rights of the woman, I'll be referring primarily to her). So while you may have the right to kill someone in self-defense if they are on your property and threatening you, in essence abortion is more like dragging someone onto your property, then killing them and claiming self-defense.
Her first thought experiment is as follows: "...suppose you and your wife are going on a romantic road trip to a cabin in the mountains. You know there is a chance that you will get into an accident and injure someone, but you are a good driver and you follow all the rules of the road. You are in a residential area and a child is obliviously playing with a ball. He runs out from behind a parked car and you hit him. He is rushed to the hospital. He is okay except for his kidneys, they are severely damaged and he needs a transplant or he will die. Although you took precautions in order to avoid a situation like this, you have still caused someone to need you to survive so a government worker visits you at your home and informs you that if you do not donate your kidney to the child you may face jail time. You don't want to have a criminal record so you agree to donate. You have to undergo surgery. You have to take a few months off work, so you are now in a terrible financial situation. Your wife leaves you and everyone around you looks down on you because you ran over a kid."
Now one thing bears mentioning. I highly doubt that if a guy accidentally hits a kid while driving and faces financial hardship, that his wife would leave him and people would look down on him. I know that she's trying to make this analogous to pregnancy, but if this is how people treat pregnancy then they really need to change their perceptions of it.
This thought experiment ignores two key factors: First, where is the responsibility located? Why was this kid just playing around the street without his parents supervising him? It seems to me that in this case, the parents are responsible for letting their kid play around the street and possibly getting hit. The man who hit the kid would probably feel horrible, but it doesn't seem to me that the situation would be his fault unless, of course, he was driving recklessly (and the point of this thought experiment is that the driver is being "safe").
Second, there is a distinction between driving and having sex. Driving a car is not an act that leads to running over people as the act of sex leads to pregnancy. No one should be hit by cars if all people are acting responsibly and being safe on the road, but sex is an act that intrinsically (that is, by the very nature of the act) leads to pregnancy. Even if you are being "safe," you are merely adding a barrier to pregnancy, you are not changing the nature of the act. 
The right to life, properly understood, is a negative right not to be killed unjustly. There is something else we must keep in mind, that the act of donating a bodily organ may be similar in some respects, but not in relevant ones. For example, pregnancy is a natural process. There are some bodily changes that occur to the woman during pregnancy, but these are all changes that her body has been adapted to handle. In contrast, organ donation is a recent phenomenon; no one's body is naturally adapted to handle organ donation, and as a result, donating an organ is a more dangerous act. Even if we take the position that a woman can't legally abort a pregnancy, we would not necessarily be committed to the position that people should be forced to donate organs. But if someone is responsible for someone's damaged organ, then I think a legitimate case can be made. But in any case, continuing with pregnancy (assuming it's not a life-threatening pregnancy) is a morally obligatory act, not supererogatory, as pro-choice advocates need it to be. Organ donations are supererogatory acts, morally heroic but in no way obligatory.
Slippery When Wet Sign
As for her second thought experiment: "Suppose I run a small coffee shop and I fail to put up a 'slippery when wet' sign and a customer trips, falls, and gets impaled on a straw. It goes right through his kidney! He can survive for now, but he will eventually need a transplant. There is a very long waiting list for the next kidney and there is no chance that he will get one in time. Does he now get to sue me for my kidney?"
I would hate to see the coffee shop that uses such dangerous straws! But at any rate, again, you are not obligated to give up your kidney. Putting up a sign is a nice warning, but you are not responsible for the patron's slipping and falling. Presumably he can see the water on the ground, and presumably he knows that water makes things slippery. Suing for a kidney in this case would be about as frivolous a lawsuit as they come.
I just don't see that her thought experiments here show that the responsibility objection fails, especially since there are some key elements to the responsibility objection that she has overlooked.
 I owe Christopher Kaczor and Frank Beckwith for my thoughts in this paragraph.