It is difficult to open a newspaper in Asia and the United States these days without reading about the Thucydides trap, the theory which posits how a rising power is predestined to go to war with an established one. In the 21st century, Thucydides has become fashionable shorthand for the coming clash between China and the US.

But there is another geo-strategic dilemma identified by the general-cum-historian of ancient Greece that more accurately captures Asia's inflection point. It is dangerous to build an empire, Thucydides warned; it is even more dangerous to give it away.

This "other Thucydides trap" encapsulates the real quandary facing the US in East Asia. The US can stand its ground and fight, at potentially massive cost. Or it could leave, retreat from East Asia after more than seven decades as the region's great power, potentially trailing chaos in its wake.

The "other Thucydides trap" also brings with it a more existential debate, one that Mr Donald Trump exploited in his successful run for the White House. What is the US military still doing in Asia more than 70 years after the end of the Pacific war anyway? Why can't Asian nations get on with each other, independent of the US?

In recent months, Asian geopolitics has been dominated by North Korea's threats to fire a nuclear-tipped missile at the US, a crisis driven by paranoia in Pyongyang, paralysis in China and fury in faraway Washington.

But Pyongyang's pyrotechnics obscures the bigger drama playing out in the region, of Asia's post-war order slowly cracking and coming apart. At the heart of this crack-up is the poisonous relationship between Asia's two indigenous superpowers, China and Japan.

The US military never left Japan, and Asia, after the war, which, on the face of it, would seem to be imperial overreach of the most overbearing kind. With its sprawling armed footprint, Pax Americana has had a stunning upside in the region, underwriting an explosion in wealth not matched since the Industrial Revolution.

Since the 1950s, Japan, and then South Korea, Taiwan and China, along with South-east Asia, were able to put bitter political and historical enmities aside to pursue economic growth.

Mr Trump ran for the White House with a darker view of Asia's renaissance. He criticised Japan and South Korea for free-riding on US security and said both countries should acquire nuclear weapons if they wished to reduce their reliance on Washington. On trade, he singled out China and Japan for cheating Americans, in league with the domestic Visigoths of globalisation, Wall Street and big business.

In doing so, he tapped ruthlessly into grassroots anger by hammering what is perhaps the most potent critique of Pax Americana: not only has the US protected Asia's flourishing economies, it has opened the American market to their exports in ways they would never reciprocate.

China's rise, or more accurately its re-emergence, has only raised the stakes in East Asia for Mr Trump and whoever might come after him in the White House.

China and Japan are global economic powers, backed by robust, advanced militaries. Along with South Korea and Taiwan, and Singapore to the south, they sit at the nexus of the tightly integrated seaborne trade network that sustains global business and US consumption. Any clash between China and Japan would not be a simple spat between neighbours. A single shot fired in anger could trigger a global economic tsunami, engulfing political capitals, trade routes, manufacturing centres and retail outlets on every continent.

That scenario, in turn, underpins a second paradox. While keeping the peace, the US presence in East Asia has papered over serial diplomatic failures. Seven decades into Pax Americana, all of the frozen-in-the-1950s conflicts buried during the decades of high-speed growth are resurfacing.

China and Taiwan, for all their tens of billions in two-way trade and personal interaction, have drifted further apart politically. The Korean peninsula remains divided along Cold War contours and bristling with conventional and nuclear armoury. The Sino-Japanese rivalry overflows with bitterness and mistrust, despite a business relationship that is one of the most valuable in the world.

Far from allowing the US to simply pack up and go home, as Mr Trump suggested, Asia's success has only magnified the dangers of an American drawdown. "It is not only true that China changed the status quo by getting strong," said Professor Yan Xuetong, one of China's most prominent hawks, "but also America and Japan changed the status quo by getting weak."

Most accounts of Sino-Japanese relations paint the two countries' differences as the inevitable result of Japan's invasion and occupation of China in the 1930s and through World War II until Tokyo's surrender in August 1945, followed by an extended squabble over responsibility for the conflict.

Alternatively, their clash is depicted as a traditional great-power contest, with an ascending superpower, China, running up against a now weaker rival competing to dominate the Asia-Pacific.

A third template takes a longer view, one of a China bent on rebuilding the ascendancy the celestial kingdom enjoyed in Asia in imperial times.

None of these templates alone, however, captures the tangled emotions and complex psychology of the Sino-Japanese relationship, nor the contemporary geopolitical dimensions of their enmity. China-Japan tensions have a long tail that extends way beyond their differences over disputed islands and wartime history.

Then, there is the question about Asia more broadly, and why political and cultural solidarity has so far eluded the region.

However attractive in theory, Asian unity has always foundered in practice. Absent the US, China has the size, ambition, wealth and military might to play a dominant role in the region for decades to come, and the mindset as well. Mr Trump's isolationist rhetoric only strengthened Beijing's hand.

But old hierarchical habits die hard in Asia. China was never enthusiastic about building up Asian institutions while Japan was the region's largest economy. Likewise, Japan's enthusiasm for the Asian project diminished once China replaced it as the region's dominant power. In other words, as long as China fails to build trust with its neighbours like Japan, the US will be invited to stay in Asia. China, for all its ambitions, is not ready to take its place.

• The writer is a Washington-based journalist and author. His book, Asia's Reckoning: The Struggle For Global Dominance, was published by Allen Lane this month.