Good question. Here is the answer in a rather lengthy form that I have posted before on FR.
First of all, they are NOT "the press." They are corporate media organizations (CMOs).
The press in the Constitutional sense is a device that can be used by people to publish their thoughts and opinions.
Every American, including those who run or work for CMOs, has a right to freely use a press to disseminate his or her views on any subject at any time.
But the reporters at NPR, NYT, Washington POS, CNN, MSNBC and all the other networks (including Fox News) do NOT have any constitutional right to have access and be heard at White House "Press" conferences.
They don't have that right, because neither I nor anybody else who posts opinions in print, by broadcast or online has that right, even though we use the press to publish our opinions, as I do regularly on Free Republic. (After all, the Internet is a means of publishing thoughts and opinions and therefore is a "press" in the Constitutional sense.)
And another "right" that these CMOs definitely DO NOT have, is the right not to be insulted by the President, who did not surrender his own First Amendment right to free speech when took the oath of office.
Being invited to participate in a White House "press" conference is therefore a privilege that can be extended or withdrawn purely at the discretion of the White House (or Congress, or the Judiciary in their own venues).
I so wish that at Trump's next "press conference," he will state this reality once and for all. And then I hope he will take a question from Jim Acosta, after prefacing it with the following statement:
"I'm going now to take a question now from Jim Acosta purely as a courtesy, albeit an undeserved one, because this is going to be his last White House 'press conference' during my administration. Additionally, I am revoking the press credentials of CNN,the racist New York Times, and a number of other Corporate Media Organizations who will soon be notified of their change in status. OK Jim, what's your question?"
Then I hope that in the future the White House will issue "Media Passes" to other respectable press users - bloggers, authors, YouTubers, etc. who will be invited to future Media Conferences, provided that they show courtesy, intelligence and respect.
And as for the CMOs, they can watch the President's Media Conferences on C-SPAN and then write whatever the hell they want to about them.
Good answer.
At the time of our Constitution, there were only two ways to communicate.
You either said it, or you wrote it.
Thus the language said “freedom of speech and of the (printing) press”.
Say what you want, and print what you want.
It never was meant to apply to an elite group of people.
Back then they were thinking about things like
Ben Franklin’s “Poor Richard’s Almanac”.