At a press conference, it is the role of the press to ask questions and write down answers. They might stage their questions with an initial statement, but it is NOT their place to answer their own question or to pass judgement on the person hosting the conference. If they want to do that, they are free to do so on their own time when they're hosting their own show, or in an editorial.
On a semi-related subject, I'm now finding it very difficult to find a video clip of the exchange that starts at the start. For some reason, every snippet with Acosta that's easily found on either YouTube or Google (same company!) trims off Acosta's first sentence.... where he was aggressive and rude. Instead, they start with Trump already being annoyed. I'll have to track down the video I posted to Pope on the day of the conference.
Okay, here it is. http://www.youtube.com/watch?time_continue=7&v=zdFe-LmFRV8

ACOSTA: "I want to challenge you on one of the statements you made at the tail end of the campaign... in the midterms."
TRUMP: "Here we go."

At that point, Acosta has already overstepped his bounds. He's not there to ask questions as might a journalist... he's there to debate and "challenge" the President of the United States... as might a talk show host or political opponent.
The President should have stopped Acosta right there - as he should with other reporters who behave similarly in future press conferences. This wasn't a talk show, or interview, or debate. It was a Presidential press conference. Acosta chose to use it as an opportunity to seize the bully pulpit. His conduct from the very start was abysmal.
I hope he enjoys being the next Megyn Kelly (which he won't be since Kelly's former network, NBC, has probably learned its lesson.)