A woman in Beijing holds her newborn daughter. (Ed Jones/AFP/Getty Images)

China is relaxing its 34-year-old one-child policy, which prohibits most families from having more than one child. Parents who themselves do not have siblings are now permitted to have two children, a change that one demographer estimated could boost the birthrate by about 10 percent. It's a big deal for human rights in China, as well as for the country's economic and demographic future.

The policy is controversial for a number of reasons, but maybe the one that Americans hear about most is the practice of forcing abortions on mothers who become pregnant with an unapproved second child. And that may get to the biggest misunderstanding that most Americans have about the policy: why these things keep happening. As my Beijing-based colleague William Wan writes in an insightful explainer, "practices of forced abortions, infanticide and involuntary sterilizations [are] all banned in theory by the government," but they still happen. They're no longer frequent, but they do happen.

In July 2012, for example, a 23-year-old mother became pregnant with her second child. Local officials arrested her, seven months into her pregnancy, and demanded her family pay $6,000 in fines for violating the one-child policy. When the family couldn't get the money together, the officials gave her an injection that killed the baby, whom the mother delivered stillborn while in police custody. It became an international news story when the mother, outraged at her child's death and at the indignity of being forced to wait alongside the body, posted a gruesome photo of the scene on social media. In China, it generated a national debate over the question, Why is this still happening?

The awful persistence of forced abortions, sterilizations and infanticide in China reflect a contradiction in the Chinese system -- and in the one-child policy itself. The senior leadership in Beijing may set national policy, such as today's relaxation of the one-child policy, but it's local- and provincial-level officials who choose when, whether and how to actually enforce those policies. If those mid-level officials want to do things differently -- say, in the above case, by continuing to use forced abortions to control birthrates, even though Beijing banned that years ago -- they often do.

This is probably the thing that Americans most misunderstand about China: It may be run by a giant authoritarian bureaucracy, but the system can get really messy. The people at the top have a lot less control over mid-level officials than outsiders often assume. Local officials will sometimes go their own way. So the question for Beijing becomes, How do you steer all those local officials to do what you want? The one-child policy is a study in how that can go wrong.

Here's the contradiction in the one-child policy: Chinese officials want to keep down the birthrate, which is why they enacted the policy in 1979 and have kept it ever since. They hand out birthrate targets to provincial and local officials, telling them they'll be judged on how well they meet the goals. But they also want to forbid state officials to enforce the policy with forced abortions and sterilizations, which are rightly loathed as horrific human rights abuses.

These two policies force the hundreds of mid-level officials who run China into a dilemma: If they conclude that they can't keep down the birthrate without using forced abortions and sterilizations, which of their two orders do they disobey? Do they let the birthrate slip above target, or do they resort to officially prohibited forced abortions? Inevitably, some officials, particularly those who believe they need to hit their birthrate targets to win a promotion, will decide it's better to break the rules against forced abortions and sterilizations.

This contradiction is why human rights groups have been arguing for years that the only real way for China to end forced abortions and sterilizations is by ending the one-child policy. And they're probably right.