As soon as word spread that President Trump had fired Gen. Timothy D. Haugh, the head of the National Security Agency and U.S. Cyber Command, current and former administration officials began floating theories about why he had been let go.

Had General Haugh opposed one of Mr. Trump’s initiatives, perhaps moved too slowly on purging officers who had worked on diversity issues? Or was he a casualty of the administration’s shifting priorities to counter narcotics?

Whether any of that was true, it had little, if anything, to do with why he was fired.

General Haugh was ousted because Laura Loomer, a far-right wing conspiracy theorist and Trump adviser, had accused him and his deputy of disloyalty, according to U.S. officials and Ms. Loomer’s social media post early Friday. He was one of several national security officials fired this past week on her advice.

“I predict you are going to see some nonsense statement about some policy difference or something General Haugh wasn’t doing, but we all know what happened,” said Senator Angus King, a Maine independent who is on the intelligence and armed services committees. “Laura Loomer said it. She is the one who told Trump to fire him.”

Senator Mitch McConnell, the Kentucky Republican and former majority leader, lamented that the Trump White House had ousted General Haugh and was appointing people to Pentagon posts who were skeptical of America’s engagement with allies and the world.

“If decades of experience in uniform isn’t enough to lead the N.S.A. but amateur isolationists can hold senior policy jobs at the Pentagon, then what exactly are the criteria for working on this administration’s national security staff?” Mr. McConnell said. “I can’t figure it out.”

The criteria Ms. Loomer appears to be using as she looks to oust people she sees as disloyal is their connections to critics of the Trump administration.

In her social media post, Ms. Loomer said General Haugh had been chosen by Gen. Mark Milley, the former chairman of the Joint Chiefs of Staff, whom she called a traitor.

Ms. Loomer said General Haugh’s deputy at the National Security Agency, Wendy Noble, was close to James Clapper, a former director of national intelligence and fierce critic of Mr. Trump.

As chairman of the Joint Chiefs, General Milley reviewed the appointments of hundreds of officers to key positions. Mr. Clapper, the longest-serving director of national intelligence in the Obama administration and a senior defense intelligence official under George W. Bush, has ties to officials throughout the spy agencies.

Representative Jim Himes of Connecticut, the top Democrat on the House intelligence committee, said he had worked closely with General Haugh and never saw anything to suggest disloyalty or a lack of competence.

“I fear this is just the hourly installment in the Laura Loomer clown car aspect of this administration,” Mr. Himes said.

He said that it was important to have a detail-oriented leader at the top of the N.S.A., and that he was concerned General Haugh’s ouster could lead to policy changes.

Mr. Himes also said he was concerned that the Trump administration could try to split the jobs of N.S.A. director and head of Cyber Command.

Since U.S. Cyber Command was created, the director of the National Security Agency has led that organization. Some within the Trump administration, and veterans of his first term, want the two jobs separated. That would allow a military officer to lead Cyber Command but give the president or the defense secretary the license to name a civilian to lead the agency.

The two agencies work closely together, but have different roles. The National Security Agency penetrates telecom and computer networks overseas, collecting communications intercepts. Cyber Command conducts offensive and defensive operations on computer networks overseas. The command helps allied countries defend their networks and hunts for malware and breaches by Russia and other adversaries.

It also conducts offensive operations against the networks of adversaries to disrupt their ability to attack the United States.

A succession of N.S.A. directors have argued that one military officer should lead both agencies to improve coordination. But some Trump administration officials believe that it is important to have a civilian in charge one of the most important spy agencies.

Some Trump administration officials have been critical of the N.S.A.’s broad power to intercept phone calls overseas, because some Americans have been caught up in those efforts.

Mr. Himes said he opposed splitting the jobs. While there is an argument for separating them if done carefully, Mr. Himes said he doubted the Trump administration would proceed in such a manner. The administration was already imposing irrational cuts on the N.S.A. that were costing the agency skilled people, he said.

“Given this administration’s break-it-first-then-fix-it style of operating, I am concerned,” Mr. Himes said. “It is not the low performers or obsolete skill sets that are being fired. In many cases it is some of our most valuable people. And this very directly makes us less safe.”

Beyond the structure of the commands, some Trump administration officials want the N.S.A. to move faster on White House initiatives.

But Mr. Himes said there was no evidence the N.S.A. was slow rolling administration priorities, and he added that General Haugh was working to step up collection on drug cartels.

“I can say with certainty that the N.S.A. was reorienting its priorities,” Mr. Himes said. “In fact in some ways they were shifting in ways that made me a little concerned that the pivot to Asia and counterterrorism collection would get short-shrifted.”

Mr. King said it was deeply dangerous to remove General Haugh at a time when Chinese intelligence agencies were penetrating telecom networks and ransomware attacks backed by Russia on hospitals were continuing.

“Our country is under attack right now in cyberspace, and the president has just removed our top general from the field for no reason at the recommendation of someone who knows nothing about national security or even the job this general does,” Mr. King said.