If he stays he will never receive a trial or be allowed to face his accusers.
Either way his human rights are violated. That's why it's arbitrary detention.
It's why his indictment has been kept secret; they want to physically grab him before they have to justify, legally, the charges against a journalist who published things in the public interest. If they weren't being shady about the whole thing, he could have been charged by now - but doing so would require them to be subject to legal scrutiny. They don't want that, because they don't have a leg to stand on. They won't tip their hand officially until he's already physically in their (or their allies') custody.
POTUS is a member of the executive branch, the same branch as the federal prosecutor made tasked with arguing charges against defendants.
If that was the real concern and not merely the excuse, why bother with Sweden? The UK has an extradition treaty with the USA. Sweden’s extradition treaty with the USA “”“prohibits extradition on the basis of "a political offense" or "an offense connected with a political offense."”””