Even by the dismal standards of the Syrian civil war, the current battle for Kobani, a Kurdish town on the Syrian side of the Syrian-Turkish border, seems particularly intractable. As ISIS militants equipped with plundered American weapons have taken on poorly armed Kurdish guerrillas who can do little to stop them, there is every chance that the extremist group will strengthen its hold on Syrian Kurdistan right up to the Turkish border. Already, some four hundred have been killed, and more than 180,000 Syrian Kurds have fled across the border to Turkey—one of the largest single outflows of refugees since the conflict began.

Yet the United States and Turkey are locked in their own dispute about who should deal with the situation. While the US government concedes that its aerial bombing campaign has had little effect, the Turkish army, whose tanks are just across the border, has stood by, reluctant to support a Kurdish population it regards as hostile and allied to its sworn enemy, Bashar al-Assad. How can two ostensible allies, who are among the most powerful outside forces in the Syrian conflict, be so feckless in the face of what both declare to be a common enemy?

In fact, Kobani shows how Turkish and US objectives diverge over Syria. The US has declared its intention to destroy ISIS and defend the Kurds in Syria and Iraq, but has not involved itself directly in efforts to remove the Assad regime in Damascus. The priority of Turkey’s AK Party government, in contrast, is not to destroy ISIS but to topple Bashar al-Assad and replace him with a Sunni-dominated government sympathetic to the relatively moderate brand of Islamism favored by most Turks, and able to act as a counterweight to the Shia-dominated, pro-Iran government of neighboring Iraq. At the same time, Turkey has long been wary of the dominant group among Syria’s Kurds, the Democratic Union Party, or PYD, which does not hide its allegiance to the Kurdistan Workers’ Party (PKK), the Turkey-based Kurdish movement that has spent the past thirty years in conflict with the Turkish state. As recently as Tuesday, Turkish jets were bombing PKK positions in southeastern Turkey. Thus, the fall of Kobani might be a price worth paying for the sobering effect it would have on what Turkey deems a greater threat: Kurdish nationalism.

For the past two years the Turks have been unsuccessfully lobbying the US to intervene to protect the hundreds of non-Kurdish Syrian towns that have been ravaged by the Assad government, and not unreasonably, they question the motives behind Washington’s sudden concern for the Kurds of Kobani—as well as the implication that Turkey should send in troops where the West fears to tread.

If ISIS captures Kobani, the militants could consolidate their control of a long stretch of the Turkish border, and establish a corridor between their stronghold of Raqqa in eastern Syria and positions further West. But the Turks are not as hostile to ISIS as the West is; until recently, the Turkish president, Recep Tayyip Erdoğan, refrained from calling it a terrorist organization, and while ISIS has beheaded Western hostages, in September Turkish negotiators were able to secure the release of 49 Turkish consular staff that the group had captured. So far, ISIS has not desecrated the tomb of the progenitor of the Ottoman sultans, which lies in the governorate of Aleppo—territory it controls—and which its fanatical iconoclasm suggests it should.

Of greater concern to the Turkish government may be Kobani’s importance as a banner for the Kurds. Until recently Kobani was one of an archipelago of towns in northern Syria that was under PYD control. In the summer of 2012, the Assad regime effectively handed over much of northern Syria to the PYD rather than let it fall into the hands of Sunni Arab groups—the so-called “moderate” Sunni opposition—that Turkey has been supporting, and it has continued to pay salaries to some officials in these areas. Even as the PYD maintains a de facto non-aggression pact with Assad, it has refused Turkish demands that it mend its bridges with those same Sunni Arab groups, thus precluding the kind of anti-Assad alliance Turkey would like to build.

During a visit he made to Ankara early this month, Salih Muslim, one of the PYD’s top leaders, reportedly begged the Turks to allow anti-tank weapons across the border into Kobani. The Turkish response was to insist that the PYD break with the Syrian government, join the mainstream Sunni opposition, and dissolve its autonomous enclaves, which it, understandably, refuses to do.

All this has thrown into doubt Turkey’s efforts to solve its own Kurdish problems. In March 2013 the PKK and the Turkish government declared their shared intention to pursue a negotiated peace, but the process has hardly advanced since then, amid Kurdish accusations that Turkey has been arming ISIS and Turkish fears that the PKK/PYD, having tasted quasi-independence in Syria, will demand a similar arrangement in Turkey as well.

Hence Turkey’s punitive indifference to the recent horrors at Kobani. President Erdoğan has called ISIS and the PKK one and the same, while Turkey’s security forces seem mainly interested in preventing Kurds in Turkey from crossing into Syria to help their brethren. Refugees coming the other way have received such a cool welcome that many have gone on into Iraqi Kurdistan.

Whatever the fate of Kobani, Turkey’s complicity in its human miseries has already had fearsome effects beyond this parched, benighted bit of land, where, ninety-nine years ago, some of the survivors of the Ottoman genocide of the Armenians slogged into Mesopotamia. Last month, from his headquarters in northern Iraq, the PKK’s operational commander, Cemil Bayık, presented more evidence that Turkey had been arming ISIS, and threatened to end its twenty-month-old ceasefire if Turkey did not stop its “war” against the Kurds of Syria.

Then, on October 7, the PKK demonstrated its undimmed ability to bring chaos to metropolitan Turkey, organizing violent protests not only across the country’s Kurdish-majority region in the southeast, but also in several cities further west. These were met—again, violently—by the security forces and by members of a Kurdish Islamist group that has been useful to the state in the past. More than twenty people were killed before the PKK’s incarcerated leader, Abdullah Öcalan, reportedly sent word that the unrest should stop.

One might wonder why the Turkish government would risk endangering a peace process with the PKK that has greatly contributed to Turkish stability, improved human rights and the rule of law, and facilitated economic development. The Turks may be calculating that the PKK cannot easily abandon a process that has brought its members new political power in some Kurdish areas and allowed Kurdish nationalist MP back into the national parliament. They also seem to believe that the Kurds are due a sharp reality check as to the impossibility of replicating Syria-style autonomy in Turkey. The ISIS advance on Kobani could serve that purpose, while the contraction of the Kurdish fief pushes the nationalists onto the tender mercies of the Turkish state—as Kobani has demonstrated. Weakened by the defeats suffered by its affiliate in Syria, the PKK may be less able to resist political demands made by the Turkish government if serious negotiations are renewed toward a final settlement.

For the United States, these calculations suggest that getting meaningful Turkish cooperation on ISIS may require a renewed US commitment toward toppling Assad. Responding to pressure from Washington, the Turkish government has agreed to join the US in training “moderate” Syrian fighters on Turkish soil. But the Turks have not approved America’s request to use their base at Incirlik in southern Turkey for US attacks on ISIS. That will only happen, the Turkish prime minister, Ahmet Davutoğlu, has insisted, if the US removes its longstanding opposition to Turkish demands for a no-fly zone over northern Syria and for the establishment of secure humanitarian corridors for displaced Syrians close to the border.

As Turkey and the United States negotiate the minutiae of a war they are fighting for different reasons, the wider fate of the Kurds is finely poised. The vile situation in Kobani has become a case study in the ways that civil wars suck in neighbors and break down alliances as the innocent are put to the sword. It is also a powerful refutation of the trite adage that the enemy of my enemy is my friend. In this conflict there are no friends.