Let's get back to what this tread is all about.
Donald Trump, Private Citizen, is implicated in breaking tax laws in the State of New York when he was Donald Trump, Private Citizen.
The State of New York wants to investigate this. In order to investigate it, they need to look at his tax records. He is refusing to cooperate with the investigate.
As justification for not cooperating with this investigation, his lawyers are arguing that the President has
complete immunity from any criminal indictment or investigation during his time in office.IOW, since he is now Donald Trump, President, he is not subject to investigation or indictment by the police like every single other person in the United States of America.

In fact, his lawyers admit that, under this theory, the President could murder someone on 5th Avenue and not be indicted until he leaves office.
This is based on theory about the Constitution (not explicitly written in the Constitution itself, but an interpretation) that the Presidency is a unique office in the government, entirely unlike any other office, elected or otherwise, in our entire government. And because it is
so unique, laws that apply to every other person do not apply to him, unless Congress decides to remove him.
If Congress is in his pocket, or so divided that it can't come to a decision about him, he is free and clear to do anything he wants while in office.
This, on the face of it, seems like a ludicrous assertion. That felonies that would get any other person in the country executed cannot even be
investigated if the accused is the President. Just to make sure he isn't distracted from his job.

So Al Capone, if he had been elected President, would have been immune from killing two people with a baseball bat at a dinner party (not just one, as depicted in the movie

), because it might distract him from running the country. Unless, of course, you could convince a majority of Congress that he did it. Which would be difficult, since the Chicago police would have been prevented from even investigating his operation while he was President.

The legal principle
stinks. Just because you are President doesn't mean you are no longer a citizen of the United States, subject to the same laws that every other citizen (and non-citizen) is.
It has become an issue now because we elected a President that really doesn't respect the law. He didn't respect it when he was a Private Citizen; he doesn't respect it now.
So rather than defending himself based on facts in this case about his state taxes, he prefers to hide behind the immunity principle.
Whether he uses his immunity to murder someone or just to hide his crimes while he was a private citizen, the principle stinks.
Yes, the President should not be subject to so many indictments that he cannot do his job. But at the same time,
the Presidency of the United States should not be a way for criminals to escape prosecution--or even INVESTIGATION--of their crimes while they are in office. That is a stupid proposition. One I would think we should all agree on.