Another element of the mystery is the deftness gap. Inside the country, China’s national leadership rarely seems as tin-eared as it is when dealing with the outside world. National-level democracy might come to China or it might not—ever. No one can be sure. But from the national level down to villages, where local officials are now elected, the government is by all reports becoming accountable in ways it wasn’t before. As farmers have struggled financially, a long-standing agricultural tax has been removed. As migrant workers have become an exploited underclass in big cities, hukou (residence-permit) rules have been liberalized so that people can get medical care and send their children to school without having to return to their “official” residence back in the countryside. Whenever necessary, the government turns to repression, but that’s usually not the first response.

The system prides itself on learning about problems as they arise and relieving social pressure before it erupts. In this regard it learned a lesson earlier this year, when its reaction to the first big natural disaster of 2008 turned into its own version of Hurricane Katrina. Unusual blizzards in central and southern China paralyzed roads and rail lines, and stranded millions of people traveling home for the Chinese New Year holidays; the central government seemed taken by surprise and was slow to respond. That didn’t happen with the next disaster, three months later. When the Sichuan earthquake occurred, Premier Wen Jiabao was on an airplane to the stricken area the same afternoon.

So I return to the puzzle: Why does a society that, like America, impresses most people who spend time here project such a poor image and scare people as much as it attracts them? Why do China’s leaders, who survive partly by listening to their own people, develop such tin ears when dealing with the outside world? I don’t pretend to have a solution. But here are some possible explanations, and some reasons why the situation matters to people other than the misunderstood Chinese.

There is no politer way to put the main problem than to call it “ignorance.” Most Americans are parochial, but (surprise!) most Chinese and their leaders are more so. American politicians may not be good at understanding foreign sensitivities or phrasing their arguments in ways likely to be effective around the world, as foreigners have mentioned once or twice in recent years. But collectively they understand that America is part of an ongoing, centuries-long, worldwide experiment and discussion about political systems and human values, and that making their case well matters.

After the 9/11 attacks, America went through a round of “Why do they hate us?” inquiry. Whether or not that brought the United States closer to understanding its problems in parts of the Islamic world, it did represent a more serious effort to understand how the country was seen than anything I have heard of in China. When the Olympic torch relay this spring was plagued by boos and protests over Tibet in places ranging from France to the United States, the reaction at every level of the Chinese system seemed to be not just insult but genuine shock. Most Chinese people were familiar only with the idea that China has always been a generous elder brother to the (often ungrateful) Tibetans. By all evidence, no one in command anticipated or prepared for this ugly response. The same Pew survey that said most Chinese felt good about their country also found that they thought the rest of the world shared their view. That belief is touching, especially considering how much of China’s history is marked by episodes of its feeling unloved and victimized. Unfortunately, it is also wrong. In many of the countries surveyed, China’s popularity and reputation were low and falling. According to a report last year by Joshua Cooper Ramo of Kissinger Associates, most people in China considered their country very “trustworthy.” Most people outside China thought the country was not trustworthy at all.