"If left unchallenged, the actions of the White House would create a unsafe chilling effect for any journalist who covers our elected officials", CNN said.
That contact has been widely debated, with CNN downplaying it, while the White House said it was a physical assault on the woman, and used that as one justification for revoking Mr. Acosta's press pass.
But Trump has made attacks on the press a core part of his political agenda, from when he campaigned on a promise to "open up our liberal laws" so he can sue media organizations, to his repeated labeling of the press as "the enemy of the people".
The Trump administration argued that Acosta didn't have any right in the first place to a press pass because the White House doesn't consider Acosta an "otherwise eligible journalist" - that is, a journalist who otherwise doesn't pose any physical threat.
As CNN said in court documents filed Tuesday, the White House denied Acosta's application for a day pass on November 8, the day after his hard pass was revoked following the post-midterms news conference. President Nixon's battles with the news media were legendary, and much more recently President Obama had an openly antagonistic relationship with Fox News. "You are a rude, awful person; you shouldn't be working for CNN", Trump told Acosta.
Prince Charles celebrates 70th birthday
The photos were scheduled to be released on November 14 when he turns the milestone age, but they leaked early on November 13. Prince William and Duchess Kate stand alongside newlyweds Prince Harry and Meghan , having an equally good time.
Fox News has long benefited from it's unique relationship to the President.
"The stated rationale for the revocation of Mr. Acosta's pass-that he was disrupting press proceedings-is evident from the video he has proffered, is entirely viewpoint- and content-neutral, and clears this limited bar [prohibiting arbitrary and less than compelling reasons]", the administration argued.
"It would be awful for the public, and for our democracy, if reporters questioning the president had to operate under an ever-present threat of this kind of retaliation", said the institute's executive director Jameel Jaffer.
"This is just more grandstanding from CNN, and we will vigorously defend against this lawsuit", Sanders said.
She alleged that Acosta "physically refused to surrender a White House microphone to an intern", softening the earlier misconduct accusation and then casting blame on the journalist for his persistent questioning.
Acosta's press pass to access the White House was suspended "until further notice" after he engaged in the contentious back-and-forth last week over the migrant caravan working its way up through Mexico. While the suit is specific to CNN and Acosta, this could have happened to anyone.
They are also seeking a declaration that the president's action was "unconstitutional, in violation of the First Amendment and the Due Process Clause of the Fifth Amendment".