The U.S. prioritized maintaining a stable Iraq over supporting Kurdish independence during and after the 2003 invasion.

Explanation: After rebelling for the second time against Saddam Hussein during a period of hostilities with the USA during the invasion of Iraq in 2003, the Kurds did managed to shake free of their genocidal oppressor! Surely, being instrumental in the swift and low-casualty victory of the invasion of Iraq means that Kurdish ambitions for a free Kurdistan can finally be realized! … unfortunately, the USA was more interested in having a ‘friendly’ Iraq than creating a sovereign Kurdistan - especially since a sovereign Kurdish state would displease another US ally in the region, Turkiye. While some amount of autonomy was granted to Iraqi Kurdistan, it still remained very far from the hopes of the Kurdish nationalists who had been fighting for the past ~40 years for independence. The Kurds have a saying - “No friends but the mountains” - from the realization of many incidents like this, wherein larger powers have used Kurds and then discarded them or given only minor support to Kurdish interests.

Explanation: After rebelling for the second time against Saddam Hussein during a period of hostilities with the USA during the invasion of Iraq in 2003, the Kurds did managed to shake free of their genocidal oppressor! Surely, being instrumental in the swift and low-casualty victory of the invasion of Iraq means that Kurdish ambitions for a free Kurdistan can finally be realized! … unfortunately, the USA was more interested in having a ‘friendly’ Iraq than creating a sovereign Kurdistan - especially since a sovereign Kurdish state would displease another US ally in the region, Turkiye. While some amount of autonomy was granted to Iraqi Kurdistan, it still remained very far from the hopes of the Kurdish nationalists who had been fighting for the past ~40 years for independence. The Kurds have a saying - “No friends but the mountains” - from the realization of many incidents like this, wherein larger powers have used Kurds and then discarded them or given only minor support to Kurdish interests.