[Swordmaker]

Berman didn't like the way Barr handled it since Barr doesn't really have the authority to fire him, and he also wanted to keep his people in the post.

Who told you that the Attorney General doesn’t have the authority to fire Berman? He just proved he does. If the president refused to back his AG in this, the AG would have no recourse but to resign immediately. Not supporting the Attorney General would demonstrate the President had no confidence in the AG, and would completely undermine his authority to run the Department of Justice.

[semimojo]

Who told you that the Attorney General doesn’t have the authority to fire Berman?

It's the DOJ's position.

Your inquiry also asks whether the Attorney General has that power. We answer this questions in the negative in view of our interpretation of § 541(c) as constituting—at least in part—the specific exercise of legislative power under Article II, section 2, clause 2, vesting in the President the power of removing a court-appointed U.S. Attorney.

Barr acknowledged as much when he came back and invoked the President in his second letter.

Not supporting the Attorney General would demonstrate the President had no confidence in the AG, and would completely undermine his authority to run the Department of Justice.

Of course, and the President can use the AG as his messenger to do the firing.

Barr didn't invoke the President's authority in his first letter so Berman said, sorry, but since I was appointed by the court the law says I'm in office until my replacement's confirmed.

If an appointment expires under subsection (c)(2), the district court for such district may appoint a United States attorney to serve until the vacancy is filled.

Now, that's at odds with the President's presumed right to fire anyone in the Executive branch and Berman would have probably lost in court, but he could have dragged it out for quite a while.

As it is he got his preferred replacement and poked his finger in Barr's eye at the same time.