Journalism is not a crime. However, hacking is. The US government is accusing Assange of conspiring to break into a computer. Hacking is not a valid method of information-gathering, even for investigative journalists publishing government secrets. 
The US government alleges that in 2010, Julian Assange assisted former US soldier turned whistleblower, Chelsea Manning, in cracking a password to gain access to the Defense Department's Secret Internet Protocol Network. The Secret Internet Protocol Network is where the Department of Defense houses classified documents and internal communications. However, there is no indication within the indictment that Assange managed to gain entry. This is not a politically-motivated charge levied against Assange for "truth-seeking" or carrying out public interest journalism. The limited nature of the charges, which only involve Assange's hacking allegations, means other journalists need not fear reprisals for publishing government information, providing it was received through legal means.
Many of the charges fall within the protections for journalistic activity. There are two main areas of the indictment which attempt to criminalise basic journalistic practice and expose the charges as politically motivated: Conspiracy The indictment alleges that Assange conspired with Chelsea Manning to "provide information and records from departments and agencies of the United States." This is not a crime. Journalists are permitted to encourage sources to reveal information of public interest that pertains to governmental activities. Anonymity "It was part of the conspiracy that Assange and Manning took measures to conceal Manning as the source of the disclosure of classified records to WikiLeaks." Journalists are entitled to protect their sources and take steps to do so. This is a vital aspect of national security journalism and investigative reporting. Without it, sources would be more reluctant to reveal information and the press would not be able to adequately hold the government to account. Either, the wording of the indictment is clumsy, or it is deliberately attempting to broaden the charges beyond computer hacking to include a conspiracy with Chelsea Manning and the steps Assange and Wikileaks took to protect her identity. Either way, neither of these are crimes. The fact they are included in the indictment shows the US government's intention to throw the book at Assange and the political motive for the charges. Given that the charges are clearly politically motivated, the UK should not extradite Assange to the United States.
[P1] Assange allegedly broke the law by trying to hack Defense Department computers. [P2] He is facing criminal charges which are not politically motivated. [P3] Therefore, he should be extradited.
[Rejectng P2] The wording of the indictment reveals the political motivation behind the charges. [Rejecting P3] The UK should not extradite someone on politically motivated charges.