It seems they believe that for Trump to criticize them, such would violate their First Amendment rights to freedom of the press. Let us take a look at the First Amendment:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.The first thing that should stand out upon reading this is that Trump is not Congress, and is not "abridging" the freedom of the press. He is merely being very highly critical of the media, something other presidents have done throughout our history.
Another thing that should stand out is that to prevent an individual from criticizing the media, or anyone else, would certainly abridge that person's rights to freedom of speech.
So everyone needs to relax. The First Amendment is not threatened by President Trump.
We should turn our attention to why Trump is critical of the media. There are so many instances of dishonest and mistake stories in the media, that there is no space for it. The Federalist ran a story about sixteen of the false stories some time ago. One can find it here.
There are many more. The latest is the false story about Trump telling about a terror attack in Sweden that did not occur. All o f the media ran with it, although it was clear from the beginning that he just flat did not say what they reported. It did fit the anti-Trump, pro-leftwing narrative, so they pushed it as long as they could. Once the truth came out, the story was already around for long enough that it could not really be taken back. A simple reading of his speech would have made clear instantly that he was not speaking of a terror attack, but of the situation in Sweden where they have lost control of the Muslim immigrants.
A few days earlier the AP ran with a story about an unsigned memo that had been leaked from DHS. It was written by some staff member and was not adopted. AP's headlines ran alleging Trump was sending 100,000 National Guard troops to round up illegal aliens. The memo in question did not put a number on the troops at all, but AP invented the number. Looks like 'fake news" to anyone.
In addition, AP apparently forgot that it was OK with them when Obama sent Guard troops to the border a few years ago.
What is made clear is that the media bitterly opposes Donald Trump, and will say or do anything to embarrass him or take him down. That latter is their object. One has to read all of the news with that in mind.
The question remains: "What should Trump do about it?"
There are not many options, and really only one that can be used without infringing upon the First Amendment. That is to simply attack the media back, which is exactly what he is doing.
In the past, wimpy Republicans, afraid of the media and wanting to pander to them, would have said nothing. John McCain comes to mind. He let the media destroy his vice-presidential nominee without ever really standing up to them. He also wouldn't let her defend herself. Now, in his cowardly way, he is highly critical of Trump for fighting back.
Right now, it appears that Trump is holding his own by attacking the media for their bias and dishonesty. He needs to continue. If he doesn't, all that will be before the public is what the media fabricates, invents or misconstrues. He would shortly be finished.
That would eventually leave us with the government the media wants: a leftist, progressive, socialist government that they can inordinately influence. That would be a sad day for the United States of American.