Soon after Turkey officially entered the fray in Syria last month, some 350 Turkish troops marched alongside more than 1,000 US-equipped Syrian rebel forces to clear the Islamic State (ISIS) out of the Syrian city of Jarablus, north of Aleppo. The battle was over before it began: the ISIS fighters fled before Turkish tanks rolled in. But the conflict, far from being over, is about to become even more complicated.

With Turkey’s entry into Syria, the conflict there has entered a new phase—one that may vex the United States, whose partners in the anti-ISIS coalition already seem more interested in fighting one another. Turkey is not, after all, interested only in clearing ISIS from its borders; it is also—and perhaps more —focused on taking down the Kurds.

To be sure, Turkey does not want ISIS anywhere near its borders. The group has carried out a series of attacks in Turkey, including a recent suicide bombing in Gaziantep that left 54 dead. But it does not want the Kurdish Democratic Union Party (PYD) there either.

The PYD is the Syrian affiliate of Turkey’s Kurdistan Workers’ Party (PKK), which the Turkish government has been fighting intermittently since 1984. With the PYD in control of some 75% of the Turkish-Syrian border, Turkey fears the opening of a new front in its battle with the PKK, which has been concentrated in Turkey’s southeast since fighting resumed in 2015.

But, as with everything in Syria, the PYD’s role is complicated. The group has secured all that border territory by fighting the same jihadis whom Turkey claims to be trying to destroy. And the US, with its Special Forces and airstrikes, has played a critical role in supporting it. The conflict of interest is glaring.

The fight against ISIS now risks provoking further infighting among supposed US allies in Syria. Since completing their operation in Jarablus, Turkish troops have engaged with the PYD’s fighters east of the city. Last week, Turkish fighter jets bombed positions that the Kurds had recently captured from ISIS.

The Kurds are just as combative. Just a few days ago, PYD Co-Chair Saleh Moslem tweeted that Turkey was in the category of Jabhat al-Nusra 'and other jihadis' backing ISIS. A few days earlier, he tweeted that Turkey would be defeated 'as' ISIS. Though the Kurds remain focused on closing the 80-kilometer (49-mile) gap, largely controlled by ISIS, between their eastern and western territories, they will not shy away from fighting a Turkey that, together with Syrian rebel forces, works to thwart their efforts.

And some Syrian rebel forces seem more than willing to work with Turkey against the Kurds—and not just for the sake of obtaining more weapons and aid. Many rebel commanders take issue with the Kurds’ attempt to exploit the Syrian uprising, whose initial goal was to end nearly five decades of oppression, to advance their own interests. As the leader of the 13th Division, a Syrian rebel brigade that receives American weapons and participates in the larger Turkish operation, declared, rebel forces 'will fight anyone who places obstacles before the revolution.' The Kurds, whatever contribution they make to taking down ISIS, seem to fall into that category.

US President Barack Obama’s administration is now being forced to face up to the consequences of its own fatal mistake in Syria. In its rush to find partners to help defeat ISIS, and thus to minimise its own direct contribution in the conflict, it emboldened parties with conflicting objectives. As the CIA engaged with the rebel units, the Pentagon trained the Kurds. Meanwhile, US officials encouraged their Turkish counterparts to seize border territory from ISIS. Instead of offsetting one another, these efforts have stoked long-smoldering conflicts—and taken the catastrophe in Syria to an even more dangerous level.

The US should have developed a coherent strategy, one based on careful selection of allies and more direct US involvement. But Obama viewed involvement in Syria as an all-or-nothing proposition: either the US deployed 200,000 troops to occupy the country for decades, or it would have to leave the fight to flawed local partners, perhaps wielding US-provided weapons. As Obama put it, a limited ground operation to defeat the jihadists would only lead to 'ideological extremes.'

What Obama failed to recognise is that irredentism is just as effective at fueling ideological extremes. When the US fostered the Kurds’ unattainable dreams, they stoked the fears of an insecure Turkish leadership. As a result, the Kurds and Turks who were meeting in 2012 are now in each other’s crosshairs, and the Obama administration, which never wanted to enter Syria in the first place, is stuck in yet another Middle Eastern quagmire.

With Obama’s presidency winding down, it is unlikely that he will rethink his incongruous Syria policy. That leaves it up to his successor to find a middle ground that protects American interests, while ensuring that the US does not bear the burden of the world’s conflicts alone. With Turkey and the Kurds at each other’s throats, striking that balance will be more difficult than ever.