Beijing has resisted letting its currency rise because it depends on the cheap yuan to drive its export-heavy economy. China has balked at stiff sanctions to rein in Iran’s nuclear ambitions because it needs access to Iran’s oil and gas fields to fuel its own growth. Beijing doesn’t want to curb carbon emissions because its ability to lift hundreds of millions of people into the middle class over the coming years is directly linked to its increased use of energy.

And, finally, Beijing has recoiled at reining in its unruly neighbor to the east, as the Obama administration implored it to do last week, because it doesn’t want to destabilize North Korea’s secretive, hermit regime to an extent that could lead to the government’s collapse and the North’s eventual reunification with South Korea.

“China isn’t 100 percent on board with U.S. efforts,” said Andrew L. Oros, an Asia expert at Washington College, in Chestertown, Md., because Beijing is “concerned with the idea of a unified Korea with U.S. troops stationed there.”

That concern has left a succession of American governments attempting the impossible.

“Basically, the U.S. wants China to do what the U.S. wants it to do,” said Rodger Baker, vice president for strategic intelligence at Stratfor, a geopolitical risk analysis company. “We want to make sure that the world stays as the United States would like to see the world. Which means making China subservient to us in some cases. In the case of North Korea, the Chinese see it as the United States pushing its policy on China and not allowing the Chinese to make their own policy, while removing from China one of the tools that it has decided it needs for its own interests.”

In this case, that tool would be a divided Korea, with a North Korea that is beholden to and wholly dependent on China serving as a buffer against American encroachment in China’s backyard.