The first amendment guarantees freedom of the press. why would the supreme court allow the government to limit this freedom

The main reason why the Supreme Court would allow the government to the limit this freedom is because sometimes speech can be dangerous to the public. An example of this would be that it's illegal to yell "bomb" on an airplane. 

There are four basic stages at which freedom of the press has been or can
be limited: (1) access to information; (2) prior restraint on publishing
information (censorship, injunctions); (3) liability for publishing (libel and
invasion of privacy suits, fines and imprisonment); and (4) requiring
reporters to testify or otherwise disclose sources or materials gathered in
the course of their employment. While this fourth category technically does
not abridge freedom of the press-it does not bar access or prevent or punish
publications-the “chilling effect” it has upon the ability of reporters to
function and to gain their sources’ confidence certainly merits its inclusion.