In previous questions, this questioner has asked about censorship of the media in issues like those of national security. He has also been asking about various approaches to censorship such as formal and informal approaches. I will answer in that light.
The major problem with that sort of censorship is that it sets up a legalistic, rule-driven, and perhaps adversarial approach to censorship. The government sets up specific rules about what may or may not be published and requires the media to abide by them. In such a situation, the media will likely feel that it is not a willing partner in the censorship (as it would if censorship were informal). The media might then approach this as if the government and its rules were the enemy. The media would search for loopholes and would try to publish as much as it possibly could.
This would be in contrast to a system of informal censorship where the media and the government are essentially partners. In this system, the media is less likely to try to evade government rules and publish sensitive information. Thus, a major problem with formal censorship is that it may well encourage the media to try to evade the rules as much as possible. This could end up causing the media to print sensitive information that it would have withheld in a system of informal censorship.
Numerous scholars have grappled with the problem of censorship, and historically, the arguments against it have fallen into several different categories. First, some have argued that open and free discussion is crucial for the discovery of truth, or from a more pragmatic standpoint, the best possible conclusion. This argument, perhaps first expressed by John Milton in Areopagitica, was echoed by John Stuart Mill and later Oliver Wendell Holmes. By this way of thinking, society as a whole is hurt by censorship.
Others, including Mill, simply argue that democracy is based on debate, and if the people are to make political decisions, then they must be free to discuss their options without certain ideas being censored. Mill argued in On Liberty:
If all mankind minus one were of one opinion, and only one person were of contrary opinion, mankind would be no more justified in silencing that one person, than he, if he had the power, would be justified in silencing mankind.
Still others have asserted that free speech and expression is a natural right, to be protected rather than usurped by government. They interpret the First Amendment broadly as the instrument by which protection is provided.
These arguments have historically clashed with what some have deemed to be the public interest, and some of the most famous censorship cases that have reached the United States Supreme Court have involved censorship not of speech but of art or literature that has been deemed obscene. Here, the problem with censorship is that it is difficult to ascertain exactly what, exactly is obscene, and whether the public interest in free expression and speech is outweighed by its interest in maintaining these standards through censorship.
While the material in these cases has not typically been political in nature, some have made a "slippery slope" argument in demonstrating another problem with censorship in any form. Censoring one type of literature, thought, or art can be used as precedent to censor another.