The media doesn't.
1. “Russia Is Fake News”
Even the media should get this one. The media is so focused on their narrative, that "Trump is somehow colluding with Putin," that they can't understand when he says there is no there, there... thus fake news.
2. “This administration is running like a fine-tuned machine”
What the media describes as botched is simply the media blowing things out of proportion. The stories are damaging only as far as the hostile media expresses outrage. That outrage didn't exist for Obama when he did far worse. Remember how the media continually reported that the Trump campaign was in turmoil? It wasn't. They won.
3. “The leaks are absolutely real; the news is fake”
Completely understandable when you don't live in a fake news bubble. The leaks are real. Stop. Any problem understanding that? The news is fake. What news? The narrative that every time Trump talks to a world leader it's the beginning of WW3. That Trump is not getting along with others is the fake news.
4. “I’m not ranting and raving”
He wasn't. But the media continues to misconstrue what he says (as described here in.)
5. “Nuclear holocaust would be like no other”
He's trying to make a larger point that the media refuses to acknowledge. Good relations between the two most powerful nations, capable of wiping out life on earth, might have some benefit!?
6. “I am the least anti-Semitic person that you have seen in your entire life”
When you repeatedly, on a daily basis, call Trump an anti-semite Hitler he might feel like responding? The press, rather than dealing in facts, has taken every opportunity to portray Trump (and his family) in the most vile way possible. Frankly, he's been very cool in his responses. I'd be much more directly angry. Trump is showing considerable self control.
7. "The greatest thing I could do is shoot that ship"
It was a hypothetical. He did not indicate he would do it. But for the record, there are times when that is exactly the right response... like when Iranian ships harass our warships... there need to be consequences that deter that sort of dangerous behavior. If it comes to pass, Americans would support it.
8. “Are they friends of yours?”
It's a natural question. He pointed out he'd like to meet with them and others but some will not because it would cause the media to turn on them.
The Americans that voted for Trump get it. The media is confused because they can't see past their own fiction. They need to escape their bubble before they are completely irrelevant.