At the end of the Persian Gulf war, the United States’ refusal to aid a rebellion it encouraged in Iraq allowed Saddam Hussein to brutally crush the insurgents, leaving him in power and American allies on the ground alienated and slaughtered by the thousands.

Now, with the Kurds potentially facing a similar fate, a Pentagon official said anger within the military was deeper than at any other point in Mr. Trump’s tenure as commander in chief.

That is in part because American military officials personally know the Kurds they have been fighting alongside. They consider them friends and even, in some cases, brothers in arms. While the Kurds may not have been with the Americans in Normandy, as Mr. Trump curiously noted on Wednesday, neither were the American service members who are now in Iraq and Syria. What those service members know, military officials say, is that the Kurds have been with them in Manbij, and Raqqa, and the Middle Euphrates River Valley…

Paul D. Eaton, a retired major general and veteran of the Iraq war, was more blunt. “It takes time to build trust,” he said. “And any time you erode trust, like this, it’s that much harder to bring it back.”