In the film itself:
There's no exact explanation possible from known details, but basically you can make a rough guess:
Ritter has a "get out of jail" letter from the President so he doesn't care too much what happens - he's safe.
There's plenty of evidence of the operation (people who participated) that a single printed page - whose authenticity is impossible to prove - isn't really relevant to making a difference as to whether Ryan goes to Congress and if so, what Congress will believe.
So, fighting over the page isn't worth bothering for him.
At the same time, by not fighting, he gets the benefit of showing Ryan that he has nothing to fear and thus Ryan going to Congress will only hurt Ryan, not him.
In the early screenplay (and the original Clancy novel)
In the early screenplay (November 10, 1992 screenplay draft by Stewart - compared to the one used in the film, revised draft of at least April 20, 1994) that scene actually played very differently. There was no printer, no hacking. He took the files from the safe and copied them at CIA copy center. This is taken straight from the book's plot.
On Page 95:
INT. RITTER'S OFFICE
A last digit - the safe door springs free - Ryan opens it,
takes out a stack of files, sets them on Ritter's desk ...
INT. A COPY CENTER AT CIA
Ryan's at Xerox, feeding in documents from SHOWBOAT file... he copies the photo...
Then, on page 96, they have their confrontation, after Ryan has all the documents, goes back to his office, and THEN goes to Ritter's office to confront him.
INT. RYAN'S OFFICE
INT RITTER'S OFFICE
RYAN: I'm talking about operation SHOWBOAT, Ritter!
I don't know why that screenplay version was revised other than "let's show 37337 Haxoring" Hollywood was very sweet on back then.
IMDB's Trivia page claims: "In Tom Clancy's novel, Ryan breaks into Ritter's safe to obtain the damning documents. The filmmakers thought that was too clichéd for film and created the dueling computers scene instead", but gives absolutely no reference for that statement.