For the second time, the killing of George Floyd by a police officer has brought about a breakage between President Trump and the American military’s most senior leader.

In abruptly firing Gen. Charles Q. Brown Jr., the chairman of the Joint Chiefs of Staff in the Friday night purge at the Pentagon, Mr. Trump did not publicly give a reason. In fact, the four-star fighter pilot with 40 years of service was at the border tending to one of the president’s highest priorities when he was dismissed.

But privately, Trump advisers point to a video that General Brown recorded in the furious days after George Floyd, a Black man, was killed by a police officer in May 2020, an act that sparked a social justice movement. In the four-minute video, General Brown reflected on his experiences as an African American pilot in the Air Force.

The killing of Mr. Floyd also blew up the relationship between Mr. Trump and General Brown’s predecessor, Gen. Mark A. Milley.

Days after Mr. Floyd’s death, General Milley, wearing his Army fatigues, accompanied Mr. Trump in a walk across Lafayette Square near the White House for a photo op after an aggressive clearing of a peaceful demonstration. General Milley was widely criticized for allowing Mr. Trump to drag him into politics.