Jeff Sessions recused himself because he had spoken with Russian governmental officials and thought the Mueller investigation was founded on legal grounds. I disagreed with him on both counts because the Mueller investigation was blatantly and obviously founded on illegal grounds. There was no reason to recuse himself concerning a fraudulently based investigation.
Now, I don't care much concerning Jeff Sessions. It was his call. As far as Donald Trump criticizing Sessions and firing Sessions over the recusal, Trump can fire Mueller directly. He can also fire Rod Rosenstein for having appointed Mueller. Trump could have done both things all along. He doesn't need an Attorney General or deputy to fire someone in his administration that an underling can fire. He has cause and the authority.
There are debates as to whether Trump could do it. However, Trump has a sworn duty as the highest official in the land to preserve, protect, and defend the Constitution from all enemies, both foreign and domestic. Trump would be able to justify his actions regardless of any arguments to the contrary because Trump has the evidence that the investigation was started on fraudulent grounds. In other words, Trump, as President, trumps all subordinates who might claim that the investigation is legit.
Within the executive branch, Trump is as the Supreme Court is in the judicial branch. If a so-called "Constitutional crisis" were to develop, the Supreme Court would back Trump anyway for exercising his supreme, executive responsibility vis-a-vis the Constitution.
An underling in the administration or executive branch cannot use a subordinate law to trump the Constitution's fundamental purpose. It's the same principle as when a local ordinance or regulation runs afoul of the state's law or the state's law runs afoul of the federal law.
Trump can't sit idly by while a regulation is used to conduct a coup by means of a fraudulent investigation. To think otherwise is just very bad lawyering.
As for Acting US Attorney General Matthew Whitaker, he didn't interact with Russian governmental officials in the lead-up to the election. More importantly, he is not, and never has been, under any obligation to treat the fraudulent Mueller investigation as legitimate. He knows this.
Trump had the legal right to appoint him as acting AG. Trump and Whitaker can wait until Whitaker receives the Senate's consent, Whitaker can act now, or Trump can act now.
If I were Trump, I'd have never let the thing get going. Trump did let it get going, but he does now have even more proof that the investigation was, and remains, a fraud: an ongoing attempt to illegally overthrow the government: a coup against the office of the President.