WITH so much in common, Japan and South Korea should be natural partners. Industrialised democracies and firm American allies, they face the same strategic threats: a nuclear-armed North Korea and a rising China. Japan’s emperor even claims Korean ancestry. Resentment at the Japanese occupation of Korea from 1910-45 should be fading. Yet the shadow of the past seems to grow darker by the year. Relations are at their lowest ebb since the two countries normalised relations in 1965. And, worryingly for America, officials in both expect worse to come.

Having snubbed Shinzo Abe, Japan’s prime minister, at two regional summits last month, Park Geun-hye, South Korea’s president, said in an interview this week that she saw no point in meeting him. Yet Japan is South Korea’s second-largest trading partner. Nor does she rule out meeting Kim Jong Un, North Korea’s youthful despot, whose regime just last month threatened her country with “ruthless pre-emptive strikes of annihilation”.

In both countries, negative stories about the other are staples of the press. Each side’s diplomats ooze exasperated contempt for the other. Koreans blame Japanese politicians for repeatedly stirring up historic disputes. In Japan a senior official says the Abe administration is “sick and tired” of South Korea. The country is like a “single-issue activist”, wilfully ignoring subjects that might unite the countries in favour of those that heighten dissension.

Neither side can resist scratching old sores. Japan insists it owns the rocky islets it calls Takeshima and South Korea, which controls them, Dokdo. For Japan, it was South Korea that opened this wound, when Ms Park’s predecessor, Lee Myung-bak, visited them last year. The South Koreans accuse Japan of bellicose rhetoric over its claim. Then there are South Korean accusations that Japan has not properly atoned for its wartime crimes. On November 1st a South Korean court ruled that Mitsubishi Heavy Industries, a big Japanese firm, should compensate four Korean women who had been dragooned into working for it during the war, and the family of a fifth, who has died. This was the third such ruling, and, since South Korea says some 300 Japanese firms used forced Korean labour, there could be many more cases to come. Most painful of all is the outrage of women forced into army brothels—the so-called “comfort women”. Efforts to deal with the scandal are helped neither by insensitive remarks from Japanese politicians, nor by the government’s resort to legalistic evasions.

Japan argues all colonial-era claims were settled in 1965, when it paid $500m in compensation and aid—one-sixth of South Korea’s GDP at the time, a Japanese official points out. Moreover, say the Japanese, their politicians have often expressed remorse for wartime excesses. That none of this, in Korean eyes, amounted to a formal government apology is not Japan’s problem.

South Korea’s president in 1965, Park Chung-hee, was Ms Park’s father, a military dictator who had earned his spurs in Japan’s imperial army. Japanese officials see Ms Park’s hard line as in part her distancing herself from her father’s legacy, in a low attempt to broaden her support. Similarly, South Koreans blame Mr Abe, the grandson of a suspected war criminal who went on to become prime minister, for making things worse.

Not only has Mr Abe tolerated visits by his colleagues to the Yasukuni shrine in Tokyo—reviled by victims of Japanese aggression because war criminals are among those honoured. He is also intent on revising Japan’s pacifist constitution, to make it a “normal” country, with a normal defence policy. For critics in South Korea, this is inseparable from his “Abenomics” policies designed to jolt the Japanese economy out of its long slump. To them, the only strategy Japan has is a nationalist revival.

To many American analysts this seems ludicrously unfair. Portrayed by South Korea, as it is by China, as a paroled serial-killer, Japan has for nearly 70 years been almost a model global citizen. And Mr Abe himself has in office (so far) refrained from visiting Yasukuni, though he would like to. America is in the throes of rebalancing foreign policy towards Asia. It is obviously more than irksome that its two most important regional allies are at daggers drawn. Last year a public outcry forced South Korea to pull out of an intelligence-sharing agreement with Japan at the last minute. America would like both to see its allies doing more together, and Japan to bear more of the burden of regional security-maintenance—as Mr Abe also wants, but South Korea resists.

Who pays the bill?

America’s problem is that for Japan and South Korea, the direct costs of falling out are bearable. South Korea’s tourist industry has taken a hit, but trade and investment flows continue. Nobody expects Japan to go to war over Dokdo/Takeshima. And some trilateral co-operation with America persists—over North Korea, for example. This week the three countries met in Washington to discuss curbing the North’s nuclear aspirations. Poor Japanese-South Korean relations can scarcely be blamed for the lack of progress on the North’s proliferation.

For Japan’s military ambitions, South Korean opposition matters far less than America’s encouragement; and for South Korea the lack of “spoke-to-spoke” security relations with Japan matters less than ties with the hub, America. So, rather than making its allies susceptible to pressure to co-operate, America’s security guarantees in effect facilitate their quarrelling. A strong trilateral alliance might alarm China and cause it to rethink the backing it provides North Korea—but South Koreans worry it might also make China more hostile to Korean unification.

A comforting poll in September by the Asan Institute, a think-tank in Seoul, showed 58% of South Koreans in favour of a Park-Abe summit without preconditions. But in neither country do leaders face strong popular demands to make up with the other. Unless the dangers of their quarrels become more evident, a slide into even sharper acrimony seems unavoidable.

Economist.com/blogs/banyan