I do see the [anti-choice] movement as anti-woman, though some individuals in the movement are not. The whole idea is condescending. When nearly everyone agrees that something is so wrong it should be criminal and we need to prevent a few people whose morals are broken from doing the thing (actual murder for instance, or burglary, embezzlement, rape...) then a law is the right tool for the job. Here though, we have millions of women, up to 1/3 by some estimates, who choose to do do something that the majority of people believe is acceptable (or at least isn't "wrong"). This is a huge moral grey area. No one is clearly right or clearly wrong, we have our own views on that. Laws are absolutely the WRONG tool for this kind of job.
The anti-choice movement harms women both by actually taking away our right to make our own medical decisions and receive medical care in our best interests...but perhaps WORSE is that it's a pack of people attempting to substitute their generic judgment for that of the women affected. Women are not children, we are capable of making moral and ethical judgments on ambiguous issues.
Where I disagree with Kim is on the relative proportion of people on each side. I think that the largest majority (even is technically pro-choice) likely shares my view about abortion being (morally) undesirable; Kim doesn't explicitly acknowledge that there's a subcurrent within the pro-choice movement that sees abortion as no more a moral decision than trimming a fingernail. Overall we have to resist the temptation to ascribe the motivations of the fringe to the majority. Still, there's no question that much of the anti-choice movement's momentum comes from the zealous fringe, especially in legislative and judicial domains. As Matthew Yglesias points out, though, that way lies extreme danger for the Republicans.