Is the President acting un-presidential? Yes. Is the News acting un-news-idential? Yes.
The News is supposed to be factual truth. That's what it was when it started, that's what it was for a long time, and then it was used as a propaganda machine and now is just simply "entertainment".
The President is supposed to be courteous, calculated, well spoken, well dressed, well rehearsed, well mannered, etc. That's what it was when it started, that's what it was for a long time, then it began to be used as a tool for big business, and well now, everyone knows what its become.
So what's the problem? If the News won't or doesn't want to be completely factual and only tell the truth anymore, then there's no reason the President has to act "Presidential" either. It's not like back in the day where the President was always highly respected regardless, and what they said meant everything. In today's world, the News has just as much influence on the people, if not more than the President themselves, so who really is more wrong in this case?
Well the News doesn't have the nuclear codes you say? Want to know who else does? The CRAZY Korean leader who acts like a 10 year old and constantly threatens the world with Nuclear destruction. Yet somehow, someway, it never actually happens.
Trust me. If the News goes back to being "The News", or decides to do the right thing and call the entertainment part something other than "The News", then Trump will stop with the whole "Fake News" thing. Since that's unlikely to happen, expect seven more years of this childish behavior from both sides. The times of "you still have to do your job correctly, even though I'm not going to do mine correctly", is over.