Oh, just ***** that *****ery.
Acosta doesn't have a First Amendment right to be an ass to the rest of the press corps. CNN might have a First Amendment right to be present at briefings - I'd argue they do - but that right is not embodied in the person of Acosta, and they can assign someone else.
5th Amendment...
What crime was he punished for? What double jeopardy was he subjected to? What testimony against himself was he compelled to give? What life, liberty, or property was taken from him? What private property was taken for him without compensation?