Suppose an individual owes lots of money on a credit card. The bank quits lending him money. He must then find another lender who will provide him money despite his high level of debt. Suddenly, his interest costs are higher.
Or - China could sell our debt, probably at a loss, to a third party and purchase Euros, gold, or other commodities. The liquidation of the paper depresses the market price, which increases the effective interest rate. Notice that this soaks up money available for purchase of dollar denominated paper and does not purchase any U.S. goods or services.
And, finally, they may well view a write off of our debt as a cost of empire.