Why were the Pentagon Papers so controversial?

Answer 1

For two reasons: technically they were stolen and they embarassed the government that was hiding what they revealed. The government tried to block publication, "prior censorship" claiming national security while the people who had the papers thought the country was being damaged by the government hiding the truth.
If this sounds familar, like Bush and secrecy in the name of National Security, the Pentagon Papers controversy is part of the reason - we should have learned from the previous problems.

Answer 2

The "Pentagon Papers" was controversial because they were about politics and that is one subject that there is always controversy about. It also revealed things that the public didn't know about:

The Pentagon Papers revealed, among other things, that the government had deliberately expanded its role in the war by conducting air strikes over Laos, raids along the coast of North Vietnam, and offensive actions taken by U.S. Marines well before the American public was told about the actions, and while President Lyndon Johnson had been promising not to expand the war. The document increased the credibility gap for the U.S. government, and was seen as hurting the efforts by the Nixon administration to fight the war.