Censorship has wide appeal for a variety of reasons:

People assume that the censors will share their personal beliefs as to which ideas and forms of expression should be aired and which should be regarded as intolerable.
Almost all of us tend to overlook our cultural limitations, forgetting that a century from now our mental outlook may seem as archaic as the Victorian outlook appears today.
People may have insufficient confidence in their own convictions to believe that the latter will prevail in a free marketplace of ideas—or insufficient confidence in their fellow humans to recognize them as rational beings capable of discovering truth and objective values.
Advocates of censorship overlook its long-term negative effect on the ability of individuals to form rational, independent judgments. Such policies fail to treat people as rational beings, thereby unwittingly undermining their capacity to develop and maintain their faculty of reason.
Assuming that censorship can be limited, people fail to foresee how the apparatus and legal precedents created by such policies may eventually be diverted to the seizure of power and other highly destructive political ends.