The NYT tells readers that: "China’s leaders have grown impatient with lectures on economic policy from their chief debtor, the United States." The reason that the United States is China largest debtor is that China is buying up massive amounts of U.S. government debt and other dollar denominated assets to maintain the high value of the dollar against the yuan. By pushing up the value of the dollar against the yuan, China makes U.S. produced goods less competitive both within the United States and internationally. This is a major cause of the U.S. trade deficit. In addition, because it increases the trade deficit and lowers GDP, China's currency policy also raises the U.S. budget deficit.
Who would have more reason to give China "lectures" on its currency policy than the country that suffers most from this policy. The NYT implies that there is something peculiar about the Obama's administration's complaints given that it is a large debtor of China. Of course the whole point is that the Obama administration is complaining because China's policies have made it a large debtor.
It is worth noting that the United States does not have to beg China to change its currency policy as the article implies. It can unilaterally set an exchange rate that has a lower value for the dollar against the yuan. This would be an extraordinary measure, however if China refused to raise the value of the yuan, the U.S. government could announce its willingness to trade yuan at a higher value (e.g. 5 yuan to a dollar) than China's official exchange rate.