Muzzling the press is chapter one in the authoritarian ruler's playbook. By the Founders' design, the president of the United States is not a king or dictator. He doesn't control the media, or get to decide which reporters are assigned to cover him.
A free press isn't free if the government imposes rules on what reporters can ask and how they must ask it. That violates the First Amendment. Period.
Banning reporters from asking follow-up questions or challenging the president's statements, under threat of taking away their access to the White House, hobbles the watchdog function of the media. White House reporters will be looking over their shoulders, calibrating the consequences, every time they ask tough questions. Meanwhile, the president will be able to dodge accountability and lie to the American people with even more impunity.