A cold war wouldn't be the worst thing for either country, in theory-- at least, not for those with money and power. For them, it would have all the benefits of an actual war with far fewer disadvantages. It would give the populace a common enemy, galvanizing them and making them easier to manipulate (which would chiefly be of benefit to the U.S. government, but would also interest China, who've had an increasing dissent problem with the propagation of social media and the maturation of a generation of youth connected to the world media and enamored by the consumer-capitalist way of life). It would provide an excuse for military buildup and for trillions of dollars in military spending, including the usual pork and unaccountable expenditures. It would probably lead to an expansion of the powers of the United States' intelligence agencies and curtailments of individual freedoms, a la The Patriot Act. And, best of all, no one would even have to write off any financial losses: unlike the cold war with the U.S.S.R., there would be no Iron Curtain this time, no looming Red Threat. Chinese and American businessmen would still be doing thousand-dollar business lunches with one another while China slipped spies into our tech sector and America sabotaged China's geopolitical interests by proxy.
(I can say that last part with a measure of certainty, as it's already been happening for decades).
I'm not saying that this is necessarily what will occur, but you asked why a cold war might occur, and there you have it. The world powers have an interest in stability, but too much peace kills the fear in a population and gives them a chance to start asking themselves questions about the way things are.