"to raise doubts when we report critically about him and his administration that we can be trusted."
No one should ever trust everything they read or watch. We used to teach this to kids, "Don't believe everything you read." It is also why the works of journalists are usually not accepted as sources in academic products.
This is because the news media has a long history of shady dealings, shenanigans, and spreading outright falsehoods even when they aren't getting things wrong but acting in good faith.
News media isn't an unquestionable priesthood. Everyone should be skeptical of what they read and watch and should always do their own research.
Trump isn't doing this to the media, the media is doing it to itself.