U.S. concerns often center on the legitimate fear that China could attack Taiwan. But despite menacing Chinese military exercises meant to deter the self-ruled island from moving closer to formal independence, many experts believe that Beijing still prefers to achieve its longstanding objective of “peaceful reunification” through measures short of war. China could lose in a war and face international sanctions and supply chain disruptions. These would be economically and politically devastating, jeopardizing Mr. Xi’s prime objectives of regime security, domestic stability and national rejuvenation.

Facing economic headwinds and a shrinking population, doubts are growing that China can achieve its goal of surpassing the United States as the world’s largest economy, let alone other metrics of global leadership. There is broad recognition within China that it remains militarily, economically and technologically weaker than the United States and that further modernization depends upon continued access to international technology, capital and markets within a stable economic order. “It is impossible for America to contain the rise of China,” the influential Chinese scholar Huang Renwei has noted, “and it is equally impossible for China to quickly surpass America.”

Chinese rhetoric about global governance reform has resonated in many developing countries that also see international institutions as tilted against them. But there is little reason to believe that the C.C.P.’s self-serving, nationalist ideology will captivate the world, especially as Mr. Xi feeds mistrust with his authoritarian ways, coercive tactics against foreign businesses and trading partners and policies that increasingly smack of paranoia. China tends to be viewed more favorably in parts of the developing world. But that owes more to economics than to ideas, and its overseas investments have often been criticized for lacking transparency, saddling poor countries with debt, as well as environmental and other concerns.

The United States must continue to discourage and hedge against more threatening Chinese behavior, including bolstering Taiwan’s capacity to resist coercion. But Washington should resist being guided solely by fear, which threatens the openness and dynamism responsible for American technological and scientific leadership. Policymakers should pair deterrent threats with more robust efforts to seek a constructive relationship with China, while also protecting the core values and interests of an inclusive international order and calling on Beijing to offer more credible reassurances of its intentions.

There is no doubt that China — whatever its trajectory — poses a huge and complex policy challenge for America. But exaggerating fears of an “existential struggle” increases the likelihood of conflict, crowds out efforts to tackle shared challenges like climate change and creates a with-us-or-against-us framing that could alienate the United States from allies and much of the world.

Worse, reflexively maneuvering to outcompete or thwart China only validates hard-liners in Beijing who believe America is implacably hostile and that the only response lies in undermining the United States.

By continuing on that road, the world’s two most powerful countries may end up turning each other into the enemies that they fear.